Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130410
Francisco Alegría , Rodrigo Ponce , Juan C. Pozo
In this paper, we study the moments of semi-Markovian versions of classical birth-death processes, focusing on the so-called Quadratic Asymptotically Symmetric (QAS) birth-death processes. By means of Tauberian theorems, we provide a complete description of their asymptotic behavior. Our results show a dichotomous pattern: when the birth rate dominates the death rate, the moments grow exponentially, while if the death rate exceeds the birth rate, the moments decay slowly. This contrasts with classical birth-death processes, where moment growth and decay are always exponential.
{"title":"Asymptotics of the moments of Quadratic Asymptotically Symmetric time non-local birth-death processes","authors":"Francisco Alegría , Rodrigo Ponce , Juan C. Pozo","doi":"10.1016/j.jmaa.2026.130410","DOIUrl":"10.1016/j.jmaa.2026.130410","url":null,"abstract":"<div><div>In this paper, we study the moments of semi-Markovian versions of classical birth-death processes, focusing on the so-called <em>Quadratic Asymptotically Symmetric (QAS) birth-death processes</em>. By means of Tauberian theorems, we provide a complete description of their asymptotic behavior. Our results show a dichotomous pattern: when the birth rate dominates the death rate, the moments grow exponentially, while if the death rate exceeds the birth rate, the moments decay slowly. This contrasts with classical birth-death processes, where moment growth and decay are always exponential.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130410"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130430
Xin-Yi Chi, Qi-Qing Song
In a socially structured game with characteristic function forms, a certain coalition can organize its members as some kinds of internal organizations, and different internal organizations determine different social strengths and attainable payoffs of their members. This study introduces socially structured games with organization utilities, and proposes -core, -core, and -core of such games. The sufficient conditions for the existence of -core and -core are given for discontinuous games, and the Hadamard well-posedness of the -core of such games is proven. By introducing a collectively feasible condition and a coalitionally C-secure condition for discontinuous socially structured games, the existence of -core is also established.
{"title":"The existence and Hadamard well-posedness of cooperative equilibria for discontinuous socially structured games","authors":"Xin-Yi Chi, Qi-Qing Song","doi":"10.1016/j.jmaa.2026.130430","DOIUrl":"10.1016/j.jmaa.2026.130430","url":null,"abstract":"<div><div>In a socially structured game with characteristic function forms, a certain coalition can organize its members as some kinds of internal organizations, and different internal organizations determine different social strengths and attainable payoffs of their members. This study introduces socially structured games with organization utilities, and proposes <span><math><mi>E</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core, <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-core, and <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core of such games. The sufficient conditions for the existence of <span><math><mi>E</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core and <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-core are given for discontinuous games, and the Hadamard well-posedness of the <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-core of such games is proven. By introducing a collectively feasible condition and a coalitionally <em>C</em>-secure condition for discontinuous socially structured games, the existence of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core is also established.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130430"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130435
Ilmari Kangasniemi
Given a bounded domain , a result by Bourgain, Brezis, and Mironescu characterizes when a function is in the Sobolev space based on the limiting behavior of its Besov seminorms. We prove a direct analogue of this result which characterizes when a differential k-form has a weak exterior derivative , where the analogue of the Besov seminorm that our result uses is based on integration over simplices.
{"title":"A Bourgain-Brezis-Mironescu -type characterization for Sobolev differential forms","authors":"Ilmari Kangasniemi","doi":"10.1016/j.jmaa.2026.130435","DOIUrl":"10.1016/j.jmaa.2026.130435","url":null,"abstract":"<div><div>Given a bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, a result by Bourgain, Brezis, and Mironescu characterizes when a function <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> is in the Sobolev space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> based on the limiting behavior of its Besov seminorms. We prove a direct analogue of this result which characterizes when a differential <em>k</em>-form <span><math><mi>ω</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mo>∧</mo></mrow><mrow><mi>k</mi></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Ω</mi><mo>)</mo></math></span> has a weak exterior derivative <span><math><mi>d</mi><mi>ω</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mo>∧</mo></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Ω</mi><mo>)</mo></math></span>, where the analogue of the Besov seminorm that our result uses is based on integration over simplices.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130435"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130441
Grigory Ivanov
John's inclusion states that a convex body in can be covered by the d-dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish the following asymptotically tight inequality: For any log-concave function f with finite, positive integral, there exist a positive definite matrix A, a point , and a positive constant α such that where is the indicator function of the unit ball .
{"title":"The John inclusion for log-concave functions","authors":"Grigory Ivanov","doi":"10.1016/j.jmaa.2026.130441","DOIUrl":"10.1016/j.jmaa.2026.130441","url":null,"abstract":"<div><div>John's inclusion states that a convex body in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> can be covered by the <em>d</em>-dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish the following asymptotically tight inequality: For any log-concave function <em>f</em> with finite, positive integral, there exist a positive definite matrix <em>A</em>, a point <span><math><mi>a</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, and a positive constant <em>α</em> such that<span><span><span><math><msub><mrow><mi>χ</mi></mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mi>α</mi><mi>f</mi><mrow><mo>(</mo><mi>A</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>a</mi><mo>)</mo><mo>)</mo></mrow><mo>≤</mo><msqrt><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msqrt><mo>⋅</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>χ</mi></mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></msub></math></span> is the indicator function of the unit ball <span><math><msup><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130441"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130439
Yurii Kolomoitsev
Traditional measures of smoothness often fail to provide accurate -error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified measure of smoothness that incorporates the local behavior of a function at the sampling points through the use of averaged operators. With this new tool, we obtain matching direct and inverse error estimates for a wide class of sampling operators and functions in spaces. Additionally, we derive a criterion for the convergence of sampling operators in , identify conditions that ensure the exact rate of approximation, construct realizations of K-functionals based on these operators, and study the smoothness properties of sampling operators. We also demonstrate how our results apply to several well-known operators, including the classical Whittaker-Shannon sampling operator, sampling operators generated by B-splines, and those based on the Gaussian.
{"title":"Special measures of smoothness for approximation by sampling operators in Lp(Rd)","authors":"Yurii Kolomoitsev","doi":"10.1016/j.jmaa.2026.130439","DOIUrl":"10.1016/j.jmaa.2026.130439","url":null,"abstract":"<div><div>Traditional measures of smoothness often fail to provide accurate <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified measure of smoothness that incorporates the local behavior of a function at the sampling points through the use of averaged operators. With this new tool, we obtain matching direct and inverse error estimates for a wide class of sampling operators and functions in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> spaces. Additionally, we derive a criterion for the convergence of sampling operators in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, identify conditions that ensure the exact rate of approximation, construct realizations of <em>K</em>-functionals based on these operators, and study the smoothness properties of sampling operators. We also demonstrate how our results apply to several well-known operators, including the classical Whittaker-Shannon sampling operator, sampling operators generated by <em>B</em>-splines, and those based on the Gaussian.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130439"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130436
Ravindra Singh , Kiran Meena , Kapish Chand Meena
This paper presents general forms of Casorati inequalities for Riemannian maps and Riemannian submersions between Riemannian manifolds. Using these general forms, we obtain Casorati inequalities for Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. As a consequence, we give Casorati inequalities for Riemannian maps (resp. submersions) when the target (resp. source) spaces are real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost space forms. To support these general forms, in the particular cases when the target or source spaces are real, complex, Sasakian, and Kenmotsu space forms, we verify known Casorati inequalities for Riemannian maps and Riemannian submersions. Further, we give Casorati inequalities for invariant and anti-invariant Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. Toward information on geometric characteristics, we discuss the equality cases. We also exemplify the general forms.
{"title":"General Casorati inequalities and implications for Riemannian maps and Riemannian submersions","authors":"Ravindra Singh , Kiran Meena , Kapish Chand Meena","doi":"10.1016/j.jmaa.2026.130436","DOIUrl":"10.1016/j.jmaa.2026.130436","url":null,"abstract":"<div><div>This paper presents general forms of Casorati inequalities for Riemannian maps and Riemannian submersions between Riemannian manifolds. Using these general forms, we obtain Casorati inequalities for Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. As a consequence, we give Casorati inequalities for Riemannian maps (resp. submersions) when the target (resp. source) spaces are real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost <span><math><mi>C</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span> space forms. To support these general forms, in the particular cases when the target or source spaces are real, complex, Sasakian, and Kenmotsu space forms, we verify known Casorati inequalities for Riemannian maps and Riemannian submersions. Further, we give Casorati inequalities for invariant and anti-invariant Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. Toward information on geometric characteristics, we discuss the equality cases. We also exemplify the general forms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130436"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130437
Dan Li
We analyze the asymptotic stability in distribution of an SIRS epidemic model described by stochastic differential equations with degenerate diffusion and Markov switching. A deterministic threshold parameter Λ for disease extinction and persistence is obtained. When , the disease will eventually disappear, and the distributions of the solutions of the model converge weakly to a singular measure. If , the disease will be persistent, and by constructing a stochastically equivalent process, we establish a Markov semigroup representation of the distribution densities and demonstrate the asymptotic stability of the semigroup.
{"title":"Asymptotic stability in distribution for a stochastic SIRS epidemic model with Markov switching","authors":"Dan Li","doi":"10.1016/j.jmaa.2026.130437","DOIUrl":"10.1016/j.jmaa.2026.130437","url":null,"abstract":"<div><div>We analyze the asymptotic stability in distribution of an SIRS epidemic model described by stochastic differential equations with degenerate diffusion and Markov switching. A deterministic threshold parameter <strong>Λ</strong> for disease extinction and persistence is obtained. When <span><math><mi>Λ</mi><mo><</mo><mn>0</mn></math></span>, the disease will eventually disappear, and the distributions of the solutions of the model converge weakly to a singular measure. If <span><math><mi>Λ</mi><mo>></mo><mn>0</mn></math></span>, the disease will be persistent, and by constructing a stochastically equivalent process, we establish a Markov semigroup representation of the distribution densities and demonstrate the asymptotic stability of the semigroup.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"557 2","pages":"Article 130437"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130438
Luis Daniel Abreu , Daniel Alpay , Tryphon T. Georgiou , Palle Jorgensen
With the use of Hida's white noise space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter, we prove and make use of bounds in the complex plane for the Hermite functions; as well as a new approach to stochastic distributions. This in turn allows us to present (in Section 6) an explicit formula for an analytically continued white noise process, realized this way in the complex domain. With the use of the Wick product, we then apply our complex white noise analysis in Section 7 in a derivation of a new realization of Hilbert space-valued stochastic integrals.
{"title":"Analytic continuation of time in Brownian motion. Stochastic distributions approach","authors":"Luis Daniel Abreu , Daniel Alpay , Tryphon T. Georgiou , Palle Jorgensen","doi":"10.1016/j.jmaa.2026.130438","DOIUrl":"10.1016/j.jmaa.2026.130438","url":null,"abstract":"<div><div>With the use of Hida's white noise space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter, we prove and make use of bounds in the complex plane for the Hermite functions; as well as a new approach to stochastic distributions. This in turn allows us to present (in Section <span><span>6</span></span>) an explicit formula for an analytically continued white noise process, realized this way in the complex domain. With the use of the Wick product, we then apply our complex white noise analysis in Section <span><span>7</span></span> in a derivation of a new realization of Hilbert space-valued stochastic integrals.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130438"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130417
Juan Pablo Alcon Apaza
<div><div>We establish local boundedness and local Hölder continuity of weak solutions to the following prototype problem:<span><span><span><math><mo>−</mo><mi>div</mi><mspace></mspace><mrow><mo>(</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mn>2</mn><mi>β</mi></mrow></msup><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>Ω</mi><mo>,</mo><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo><mo>,</mo><mi>β</mi></mrow><mrow><mi>s</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo></mrow></msubsup><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace><mtext> in </mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, is a bounded domain. The nonlocal operator is defined by<span><span><span><math><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>Ω</mi><mo>,</mo><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo><mo>,</mo><mi>β</mi></mrow><mrow><mi>s</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo></mrow></msubsup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mrow><mi>P</mi><mo>.</mo><mi>V</mi><mi>.</mi></mrow><mspace></mspace><munder><mo>∫</mo><mrow><mi>Ω</mi></mrow></munder><mfrac><mrow><mo>|</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mi>u</mi><mo>(</mo><mi>y</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>−</mo><mn>2</mn></mrow></msup><mo>(</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mi>u</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi><mo>+</mo><mi>s</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>β</mi></mrow></msup><mo>|</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>β</mi></mrow></msup></mrow></mfrac><mspace></mspace><mi>d</mi><mi>y</mi><mo>.</mo></math></span></span></span> Here, <span><math><mi>p</mi><mo>:</mo><mi>Ω</mi><mo>×</mo><mi>Ω</mi><mo>→</mo><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> and <span><math><mi>s</mi><mo>:</mo><mi>Ω</mi><mo>×</mo><mi>Ω</mi><mo>→</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> are measurable functions, <span><math><mi>q</mi><mo>:</mo><mo>=</mo><mi>ess</mi><mspace></mspace><msub><mrow><mi>sup</mi></mrow><mrow><mi>Ω</mi><mo>×</mo><mi>Ω</mi></mrow></msub><mo></mo><mspace></mspace><mi>p</mi></math></span>, and <span><math><mn>0</mn><mo>≤</mo><mn>2</mn>
我们建立了以下原型问题弱解的局部有界性和局部Hölder连续性：−div(|x|−2β|∇u|q−2∇u)+（−Δ）Ω，p(⋅,⋅),βs(⋅,⋅)u=0在Ω中，其中Ω∧Rn， n≥2是一个有界域。外地操作符被定义为(−Δ)Ω,p(⋅⋅),β年代(⋅⋅)u (x): = pv∫Ω| u (x)−u (y) | p (x, y)−2 (u (x)−u (y)) x−y | | n + s (x, y) p (x, y)⋅1 | x |βy | |βdy。在这里,p:Ω×Ω→(∞)和年代:Ω×Ω→(0,1)是可测函数,问:= esssupΩ×Ωp,和0≤2β& lt; n。我们的方法是解析的，依赖于De Giorgi-Nash-Moser理论对具有可变指数和权重的混合局部-非局部框架的适应。
{"title":"Local Hölder regularity for quasilinear elliptic equations with mixed local-nonlocal operators, variable exponents, and weights","authors":"Juan Pablo Alcon Apaza","doi":"10.1016/j.jmaa.2026.130417","DOIUrl":"10.1016/j.jmaa.2026.130417","url":null,"abstract":"<div><div>We establish local boundedness and local Hölder continuity of weak solutions to the following prototype problem:<span><span><span><math><mo>−</mo><mi>div</mi><mspace></mspace><mrow><mo>(</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mn>2</mn><mi>β</mi></mrow></msup><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>Ω</mi><mo>,</mo><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo><mo>,</mo><mi>β</mi></mrow><mrow><mi>s</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo></mrow></msubsup><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace><mtext> in </mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, is a bounded domain. The nonlocal operator is defined by<span><span><span><math><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>Ω</mi><mo>,</mo><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo><mo>,</mo><mi>β</mi></mrow><mrow><mi>s</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo></mrow></msubsup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mrow><mi>P</mi><mo>.</mo><mi>V</mi><mi>.</mi></mrow><mspace></mspace><munder><mo>∫</mo><mrow><mi>Ω</mi></mrow></munder><mfrac><mrow><mo>|</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mi>u</mi><mo>(</mo><mi>y</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>−</mo><mn>2</mn></mrow></msup><mo>(</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mi>u</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi><mo>+</mo><mi>s</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>β</mi></mrow></msup><mo>|</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>β</mi></mrow></msup></mrow></mfrac><mspace></mspace><mi>d</mi><mi>y</mi><mo>.</mo></math></span></span></span> Here, <span><math><mi>p</mi><mo>:</mo><mi>Ω</mi><mo>×</mo><mi>Ω</mi><mo>→</mo><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> and <span><math><mi>s</mi><mo>:</mo><mi>Ω</mi><mo>×</mo><mi>Ω</mi><mo>→</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> are measurable functions, <span><math><mi>q</mi><mo>:</mo><mo>=</mo><mi>ess</mi><mspace></mspace><msub><mrow><mi>sup</mi></mrow><mrow><mi>Ω</mi><mo>×</mo><mi>Ω</mi></mrow></msub><mo></mo><mspace></mspace><mi>p</mi></math></span>, and <span><math><mn>0</mn><mo>≤</mo><mn>2</mn>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130417"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130421
K. Benmoussa , J. Deteix , D. Yakoubi
In this paper, we study the three-dimensional velocity–vorticity–helicity (VVH) formulation modeling the flow of incompressible Newtonian fluids. We present an analysis of the formulation that encompasses the existence and regularity of solutions, providing a rigorous functional framework in which the VVH formulation is shown to be equivalent to the more traditional velocity–pressure formulation.
{"title":"On the well-posedness of the unsteady velocity-vorticity-helicity formulation of the Navier–Stokes equations","authors":"K. Benmoussa , J. Deteix , D. Yakoubi","doi":"10.1016/j.jmaa.2026.130421","DOIUrl":"10.1016/j.jmaa.2026.130421","url":null,"abstract":"<div><div>In this paper, we study the three-dimensional velocity–vorticity–helicity (VVH) formulation modeling the flow of incompressible Newtonian fluids. We present an analysis of the formulation that encompasses the existence and regularity of solutions, providing a rigorous functional framework in which the VVH formulation is shown to be equivalent to the more traditional velocity–pressure formulation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130421"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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