Pub Date : 2026-02-01Epub Date: 2025-10-24DOI: 10.1016/j.na.2025.113984
Wojciech Górny , Michał Łasica , Alexandros Matsoukas
We consider a class of integral functionals with Musielak–Orlicz type variable growth, possibly linear in some regions of the domain. This includes power-type integrands with as well as double-phase integrands with . The main goal of this paper is to identify the -subdifferential of the functional, including a local characterisation in terms of a variant of the Anzellotti product defined through the Young’s inequality. As an application, we obtain the Euler–Lagrange equation for the variant of Rudin–Osher–Fatemi image denoising problem with variable growth regularising term. Moreover, we provide a characterisation of the -gradient flow of variable-growth total variation in terms of a parabolic PDE.
{"title":"Euler–Lagrange equations for variable-growth total variation","authors":"Wojciech Górny , Michał Łasica , Alexandros Matsoukas","doi":"10.1016/j.na.2025.113984","DOIUrl":"10.1016/j.na.2025.113984","url":null,"abstract":"<div><div>We consider a class of integral functionals with Musielak–Orlicz type variable growth, possibly linear in some regions of the domain. This includes <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> power-type integrands with <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></mrow></math></span> as well as double-phase <span><math><mrow><mi>p</mi><mspace></mspace><mo>−</mo><mspace></mspace><mi>q</mi></mrow></math></span> integrands with <span><math><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow></math></span>. The main goal of this paper is to identify the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-subdifferential of the functional, including a local characterisation in terms of a variant of the Anzellotti product defined through the Young’s inequality. As an application, we obtain the Euler–Lagrange equation for the variant of Rudin–Osher–Fatemi image denoising problem with variable growth regularising term. Moreover, we provide a characterisation of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-gradient flow of variable-growth total variation in terms of a parabolic PDE.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113984"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-21DOI: 10.1016/j.na.2025.113980
Ze-Yu Ye, Xiao-Liu Wang
In this paper, we study a generalized gradient flow of anisoperimetric ratio, whose inner normal velocity contains a power of anisotropic curvature for convex closed curves. It is shown that for any embedded smooth closed convex initial curve, the flow exists globally and the curvature of evolving curves converges smoothly to the curvature of the boundary of the Wulff shape, which is determined by the given anisotropic function, as time goes to infinity.
{"title":"Evolution of convex closed curves under the generalized gradient flow of anisoperimetric ratio","authors":"Ze-Yu Ye, Xiao-Liu Wang","doi":"10.1016/j.na.2025.113980","DOIUrl":"10.1016/j.na.2025.113980","url":null,"abstract":"<div><div>In this paper, we study a generalized gradient flow of anisoperimetric ratio, whose inner normal velocity contains a power of anisotropic curvature for convex closed curves. It is shown that for any embedded smooth closed convex initial curve, the flow exists globally and the curvature of evolving curves converges smoothly to the curvature of the boundary of the Wulff shape, which is determined by the given anisotropic function, as time goes to infinity.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113980"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-03DOI: 10.1016/j.na.2025.113953
Noemi David , Filippo Santambrogio , Markus Schmidtchen
We present regularity results for nonlinear drift–diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally study the effect of linear diffusion on our regularity result (a scenario of particular interest in the incompressible case, for it represents the motion of particles driven by a Brownian motion subject to a density constraint). Specifically, this work concerns the -summability of the pressure gradient in porous medium flows with drifts that is stable with respect to the exponent of the nonlinearity, and -estimates on the pressure Hessian (in particular, in the incompressible case with linear diffusion we prove that the pressure is the positive part of an -function).
{"title":"Uniform regularity estimates for nonlinear diffusion–advection equations in the hard-congestion limit","authors":"Noemi David , Filippo Santambrogio , Markus Schmidtchen","doi":"10.1016/j.na.2025.113953","DOIUrl":"10.1016/j.na.2025.113953","url":null,"abstract":"<div><div>We present regularity results for nonlinear drift–diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally study the effect of linear diffusion on our regularity result (a scenario of particular interest in the incompressible case, for it represents the motion of particles driven by a Brownian motion subject to a density constraint). Specifically, this work concerns the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>-summability of the pressure gradient in porous medium flows with drifts that is stable with respect to the exponent of the nonlinearity, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimates on the pressure Hessian (in particular, in the incompressible case with linear diffusion we prove that the pressure is the positive part of an <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-function).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113953"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-03DOI: 10.1016/j.na.2025.113966
Shu Wang, Rulv Li
We in this paper study the singularity formation and global well-posedness of a nonlocal model for some initial boundary condition with a real parameter, which is a one dimensional weak advection model for the three dimensional incompressible Navier–Stokes equations. Based on the Lyapunov functional and contradiction argument, we can prove that the inviscid nonlocal model develops a finite time blowup solution with some even initial data. But, for some special positive parameter and initial data with the given symbol, the inviscid model also has a global smooth solution by the characteristic’ method. Furthermore, by the energy estimations and Gagliardo–Nirenberg inequality, we also obtain that the viscous nonlocal model has a unique global solution with some initial data with the given symbol for all nonnegative parameter. More specially, there is a particular model to the nonlocal model such that the global solution to this model exists for some negative parameter.
{"title":"Global and singular solution to a nonlocal model of three-dimensional incompressible Navier–Stokes equations","authors":"Shu Wang, Rulv Li","doi":"10.1016/j.na.2025.113966","DOIUrl":"10.1016/j.na.2025.113966","url":null,"abstract":"<div><div>We in this paper study the singularity formation and global well-posedness of a nonlocal model for some initial boundary condition with a real parameter, which is a one dimensional weak advection model for the three dimensional incompressible Navier–Stokes equations. Based on the Lyapunov functional and contradiction argument, we can prove that the inviscid nonlocal model develops a finite time blowup solution with some even initial data. But, for some special positive parameter and initial data with the given symbol, the inviscid model also has a global smooth solution by the characteristic’ method. Furthermore, by the energy estimations and Gagliardo–Nirenberg inequality, we also obtain that the viscous nonlocal model has a unique global solution with some initial data with the given symbol for all nonnegative parameter. More specially, there is a particular model to the nonlocal model such that the global solution to this model exists for some negative parameter.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113966"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-07DOI: 10.1016/j.na.2025.113969
Jie Cheng , Tianrui Bai , Fangqi Chen
In this paper, we consider the Riemann problem of the Aw–Rascle traffic model with a damping term and the formation of delta shock waves in the limit of the Riemann solutions as . By introducing a new variable and employing generalized characteristic analysis methods, we construct solutions to the Riemann problem of the inhomogeneous Aw–Rascle traffic model. Specially, for the case , we prove the existence of a critical value for such that when , the Riemann solutions contain no vacuum states; otherwise, a vacuum state emerges. Furthermore, we demonstrate that as , the limit of the Riemann solutions with vacuum states aligns with the Riemann solutions to the inhomogeneous transport model under the same initial conditions, while the limit of solutions with shock waves converges to a curved delta shock solution. Notably, the weights supported on the delta shock solution differ from the Riemann solutions to the inhomogeneous transport model due to the influence of the damping term.
{"title":"Formation of delta shock waves in the limit of Riemann solutions to the Aw–Rascle traffic model with a damping term","authors":"Jie Cheng , Tianrui Bai , Fangqi Chen","doi":"10.1016/j.na.2025.113969","DOIUrl":"10.1016/j.na.2025.113969","url":null,"abstract":"<div><div>In this paper, we consider the Riemann problem of the Aw–Rascle traffic model with a damping term and the formation of delta shock waves in the limit of the Riemann solutions as <span><math><mrow><mi>γ</mi><mo>→</mo><mn>1</mn></mrow></math></span>. By introducing a new variable and employing generalized characteristic analysis methods, we construct solutions to the Riemann problem of the inhomogeneous Aw–Rascle traffic model. Specially, for the case <span><math><mrow><mn>0</mn><mo><</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msub><mo><</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></math></span>, we prove the existence of a critical value <span><math><msub><mrow><mover><mrow><mi>γ</mi></mrow><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span> for <span><math><mi>γ</mi></math></span> such that when <span><math><mrow><mn>0</mn><mo><</mo><mi>γ</mi><mo><</mo><msub><mrow><mover><mrow><mi>γ</mi></mrow><mo>¯</mo></mover></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, the Riemann solutions contain no vacuum states; otherwise, a vacuum state emerges. Furthermore, we demonstrate that as <span><math><mrow><mi>γ</mi><mo>→</mo><mn>1</mn></mrow></math></span>, the limit of the Riemann solutions with vacuum states aligns with the Riemann solutions to the inhomogeneous transport model under the same initial conditions, while the limit of solutions with shock waves converges to a curved delta shock solution. Notably, the weights supported on the delta shock solution differ from the Riemann solutions to the inhomogeneous transport model due to the influence of the damping term.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113969"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-24DOI: 10.1016/j.na.2025.113968
Ruhua Zhang , Guanggui Chen
In this paper, we establish the Hörmander type multiplier theorem for Fourier multipliers on Hardy spaces for , with regularity condition formulated in terms of modulation spaces where . We further investigate the boundedness of Fourier multipliers on Lebesgue spaces for through the interpolation. The conditions proposed in this paper not only improve those established by previous researchers but also refine the corresponding conclusions. Additionally, we introduce a novel multiplier theorem that incorporates the regularity condition formulated in terms of Wiener amalgam spaces . Here the multiplier theorem may be of methodology to further studies of Fourier multipliers.
{"title":"On the boundedness of Fourier multipliers in terms of modulation spaces regularity","authors":"Ruhua Zhang , Guanggui Chen","doi":"10.1016/j.na.2025.113968","DOIUrl":"10.1016/j.na.2025.113968","url":null,"abstract":"<div><div>In this paper, we establish the Hörmander type multiplier theorem for Fourier multipliers on Hardy spaces <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mfenced><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></math></span> for <span><math><mrow><mn>0</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>1</mn></mrow></math></span>, with regularity condition formulated in terms of modulation spaces <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>q</mi></mrow></msubsup><mfenced><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></math></span> where <span><math><mrow><mn>1</mn><mo>≤</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>≤</mo><mi>∞</mi><mo>,</mo><mi>s</mi><mo>></mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>q</mi></mrow></mfrac></mrow></math></span>. We further investigate the boundedness of Fourier multipliers on Lebesgue spaces <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mfenced><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></math></span> for <span><math><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mi>∞</mi></mrow></math></span> through the interpolation. The conditions proposed in this paper not only improve those established by previous researchers but also refine the corresponding conclusions. Additionally, we introduce a novel multiplier theorem that incorporates the regularity condition formulated in terms of Wiener amalgam spaces <span><math><mrow><msubsup><mrow><mi>W</mi></mrow><mrow><mi>s</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>q</mi></mrow></msubsup><mfenced><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></math></span>. Here the multiplier theorem may be of methodology to further studies of Fourier multipliers.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113968"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-10DOI: 10.1016/j.na.2025.113978
Antonio Arnal
We study the generator of the one-dimensional damped wave equation with unbounded damping at infinity. We show that the norm of the corresponding resolvent operator, , is approximately constant as on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, . Our proof rests on a precise asymptotic analysis of the norm of the inverse of , the quadratic operator associated with .
{"title":"Resolvent estimates for the one-dimensional damped wave equation with unbounded damping","authors":"Antonio Arnal","doi":"10.1016/j.na.2025.113978","DOIUrl":"10.1016/j.na.2025.113978","url":null,"abstract":"<div><div>We study the generator <span><math><mi>G</mi></math></span> of the one-dimensional damped wave equation with unbounded damping at infinity. We show that the norm of the corresponding resolvent operator, <span><math><mrow><mo>‖</mo><msup><mrow><mrow><mo>(</mo><mi>G</mi><mo>−</mo><mi>λ</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>‖</mo></mrow></math></span>, is approximately constant as <span><math><mrow><mrow><mo>|</mo><mi>λ</mi><mo>|</mo></mrow><mo>→</mo><mo>+</mo><mi>∞</mi></mrow></math></span> on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, <span><math><mrow><msub><mrow><mover><mrow><mi>ℂ</mi></mrow><mo>¯</mo></mover></mrow><mrow><mo>−</mo></mrow></msub><mo>≔</mo><mrow><mo>{</mo><mi>λ</mi><mo>∈</mo><mi>ℂ</mi><mo>:</mo><mo>Re</mo><mi>λ</mi><mo>≤</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span>. Our proof rests on a precise asymptotic analysis of the norm of the inverse of <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></mrow></math></span>, the quadratic operator associated with <span><math><mi>G</mi></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113978"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-15DOI: 10.1016/j.na.2025.113976
Jarosław Mederski , Jacopo Schino
We look for travelling wave fields satisfying Maxwell’s equations in a nonlinear and cylindrically symmetric medium. We obtain a sequence of solutions with diverging energy consisting of transverse magnetic field modes. In addition, we consider a general nonlinearity, controlled by an N-function.
{"title":"Travelling waves for Maxwell’s equations in nonlinear and symmetric media","authors":"Jarosław Mederski , Jacopo Schino","doi":"10.1016/j.na.2025.113976","DOIUrl":"10.1016/j.na.2025.113976","url":null,"abstract":"<div><div>We look for travelling wave fields <span><span><span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>U</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>cos</mo><mrow><mo>(</mo><mi>k</mi><mi>z</mi><mo>+</mo><mi>ω</mi><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mover><mrow><mi>U</mi></mrow><mrow><mo>˜</mo></mrow></mover><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>sin</mo><mrow><mo>(</mo><mi>k</mi><mi>z</mi><mo>+</mo><mi>ω</mi><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mi>R</mi><mo>,</mo></mrow></math></span></span></span>satisfying Maxwell’s equations in a nonlinear and cylindrically symmetric medium. We obtain a sequence of solutions with diverging energy consisting of transverse magnetic field modes. In addition, we consider a general nonlinearity, controlled by an <em>N</em>-function.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113976"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145322045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-08DOI: 10.1016/j.na.2025.113970
Chenkai Liu , Shaodong Wang , Ran Zhuo
In this paper, we obtain a priori estimates for the set of anti-symmetric solutions to a fractional Laplacian equation in a bounded domain using a blowing-up and rescaling argument. In order to establish a contradiction to possible blow-ups, we apply a certain variation of the moving planes method in order to prove a monotonicity result for the limit equation after rescaling.
{"title":"A priori estimates for anti-symmetric solutions to a fractional Laplacian equation in a bounded domain","authors":"Chenkai Liu , Shaodong Wang , Ran Zhuo","doi":"10.1016/j.na.2025.113970","DOIUrl":"10.1016/j.na.2025.113970","url":null,"abstract":"<div><div>In this paper, we obtain a priori estimates for the set of anti-symmetric solutions to a fractional Laplacian equation in a bounded domain using a blowing-up and rescaling argument. In order to establish a contradiction to possible blow-ups, we apply a certain variation of the moving planes method in order to prove a monotonicity result for the limit equation after rescaling.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113970"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-09DOI: 10.1016/j.na.2025.113965
Yasuaki Fujitani , Yohei Sakurai
We develop geometric analysis on weighted Riemannian manifolds under lower 0-weighted Ricci curvature bounds. Under such curvature bounds, we prove a first non-zero Steklov eigenvalue estimate of Wang–Xia type on compact weighted manifolds with boundary, and a first non-zero eigenvalue estimate of Choi–Wang type on closed weighted minimal hypersurfaces. We also produce an ABP estimate and a Sobolev inequality of Brendle type.
{"title":"Geometric analysis on weighted manifolds under lower 0-weighted Ricci curvature bounds","authors":"Yasuaki Fujitani , Yohei Sakurai","doi":"10.1016/j.na.2025.113965","DOIUrl":"10.1016/j.na.2025.113965","url":null,"abstract":"<div><div>We develop geometric analysis on weighted Riemannian manifolds under lower 0-weighted Ricci curvature bounds. Under such curvature bounds, we prove a first non-zero Steklov eigenvalue estimate of Wang–Xia type on compact weighted manifolds with boundary, and a first non-zero eigenvalue estimate of Choi–Wang type on closed weighted minimal hypersurfaces. We also produce an ABP estimate and a Sobolev inequality of Brendle type.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113965"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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