Pub Date : 2024-02-19DOI: 10.1142/s0219199723500657
Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented.
{"title":"Perspective functions with nonlinear scaling","authors":"Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva","doi":"10.1142/s0219199723500657","DOIUrl":"https://doi.org/10.1142/s0219199723500657","url":null,"abstract":"<p>The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072619","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 : 2024-02-16DOI: 10.1142/s0219199724500056
Amin Esfahani, Achenef Tesfahun
In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.
{"title":"Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation","authors":"Amin Esfahani, Achenef Tesfahun","doi":"10.1142/s0219199724500056","DOIUrl":"https://doi.org/10.1142/s0219199724500056","url":null,"abstract":"<p>In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Δ</mi><mi>u</mi></math></span><span></span> in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076296","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 : 2024-02-14DOI: 10.1142/s0219199723500621
Veronica Felli, Ana Primo, Giovanni Siclari
A classification of local asymptotic profiles and strong unique continuation properties are established for a class of fractional heat equations with a Hardy-type potential, via an Almgren–Poon monotonicity formula combined with a blow-up analysis.
{"title":"On fractional parabolic equations with Hardy-type potentials","authors":"Veronica Felli, Ana Primo, Giovanni Siclari","doi":"10.1142/s0219199723500621","DOIUrl":"https://doi.org/10.1142/s0219199723500621","url":null,"abstract":"<p>A classification of local asymptotic profiles and strong unique continuation properties are established for a class of fractional heat equations with a Hardy-type potential, via an Almgren–Poon monotonicity formula combined with a blow-up analysis.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072623","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 : 2024-02-14DOI: 10.1142/s0219199723500670
Eric Larson
Let be a general Brill–Noether curve. A classical problem is to determine when , which controls the quadric section of .
So far this problem has only been solved in characteristic zero, in which case with finitely many exceptions. In this paper, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic .
设 C⊂ℙ3 是一条一般的布里渊-诺特曲线。一个经典问题是确定何时 H0(NC(-2))=0，它控制着 C 的四边形截面。迄今为止，这个问题只在特征为零时得到解决，在这种情况下，H0(NC(-2))=0 有有限多个例外。在本文中，我们将这些结果扩展到正特征，在特征 2 中发现了大量新的例外。
{"title":"On the cohomology of NC(−2) in positive characteristic","authors":"Eric Larson","doi":"10.1142/s0219199723500670","DOIUrl":"https://doi.org/10.1142/s0219199723500670","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mrow><mi>C</mi><mo>⊂</mo><msup><mrow><mi>ℙ</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span><span></span> be a general Brill–Noether curve. A classical problem is to determine when <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy=\"false\">(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>C</mi></mrow></msub><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mn>2</mn><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo><mo>=</mo><mn>0</mn></mrow></math></span><span></span>, which controls the quadric section of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mrow><mi>C</mi></mrow></math></span><span></span>.</p><p>So far this problem has only been solved in characteristic zero, in which case <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy=\"false\">(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>C</mi></mrow></msub><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mn>2</mn><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo><mo>=</mo><mn>0</mn></mrow></math></span><span></span> with finitely many exceptions. In this paper, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mrow><mn>2</mn></mrow></math></span><span></span>.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072617","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 : 2024-02-01DOI: 10.1142/s0219199723500530
Andrea Santi, Dennis The
For the largest exceptional simple Lie superalgebra , having dimension , we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second- and third-order, respectively.
{"title":"Exceptionally simple super-PDE for F(4)","authors":"Andrea Santi, Dennis The","doi":"10.1142/s0219199723500530","DOIUrl":"https://doi.org/10.1142/s0219199723500530","url":null,"abstract":"<p>For the largest exceptional simple Lie superalgebra <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>F</mi><mo stretchy=\"false\">(</mo><mn>4</mn><mo stretchy=\"false\">)</mo></math></span><span></span>, having dimension <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mn>2</mn><mn>4</mn><mo>|</mo><mn>1</mn><mn>6</mn><mo stretchy=\"false\">)</mo></math></span><span></span>, we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second- and third-order, respectively.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072585","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 : 2024-01-29DOI: 10.1142/s0219199723500669
Marcin Bilski, Jacek Bochnak, Wojciech Kucharz
Let be an uncountable field of characteristic . For a given function , with , we prove that is regular if and only if the restriction is a regular function for every algebraic curve in which is either an affine line or is isomorphic to a plane curve in defined by the equation , where are prime numbers. We also show that regularity of can be verified on other algebraic curves in with desired geometric properties. Furthermore, if the field is not algebraically closed, we construct a -valued function on that is not regular, but all its restrictions to nonsingular algebraic curves in
{"title":"Algebraic versions of Hartogs’ theorem","authors":"Marcin Bilski, Jacek Bochnak, Wojciech Kucharz","doi":"10.1142/s0219199723500669","DOIUrl":"https://doi.org/10.1142/s0219199723500669","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝕂</mi></math></span><span></span> be an uncountable field of characteristic <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mn>0</mn></math></span><span></span>. For a given function <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi><mo>:</mo><msup><mrow><mi>𝕂</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><mi>𝕂</mi></math></span><span></span>, with <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, we prove that <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi></math></span><span></span> is regular if and only if the restriction <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>C</mi></mrow></msub></math></span><span></span> is a regular function for every algebraic curve <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> in <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝕂</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> which is either an affine line or is isomorphic to a plane curve in <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝕂</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span> defined by the equation <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>X</mi></mrow><mrow><mi>p</mi></mrow></msup><mo stretchy=\"false\">−</mo><msup><mrow><mi>Y</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>=</mo><mn>0</mn></math></span><span></span>, where <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi><mo><</mo><mi>q</mi></math></span><span></span> are prime numbers. We also show that regularity of <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi></math></span><span></span> can be verified on other algebraic curves in <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝕂</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> with desired geometric properties. Furthermore, if the field <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝕂</mi></math></span><span></span> is not algebraically closed, we construct a <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝕂</mi></math></span><span></span>-valued function on <span><math altimg=\"eq-00016.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝕂</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> that is not regular, but all its restrictions to nonsingular algebraic curves in <span><math altimg=\"eq-00017.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝕂</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></s","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072482","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 : 2024-01-26DOI: 10.1142/s0219199724500020
L. Bezerra, Evgeny Mukhin
{"title":"Representations of quantum toroidal superalgebras and plane s-partitions","authors":"L. Bezerra, Evgeny Mukhin","doi":"10.1142/s0219199724500020","DOIUrl":"https://doi.org/10.1142/s0219199724500020","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139593683","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 : 2024-01-24DOI: 10.1142/s0219199723500591
Inkang Kim, Xueyuan Wan, Genkai Zhang
We study Kähler metrics on the total space of Griffiths negative holomorphic vector bundles over Kähler manifolds. As an application, we construct mapping class group invariant Kähler metrics on , the holomorphic tangent bundle of Teichmüller space of a closed surface . Consequently,we obtain a new mapping class group invariant Kähler metric on the quasi-Fuchsian space , which extends the Weil–Petersson metric on the Teichmüller space . We also calculate its curvature and prove non-positivity for the curvature along the tautological directions.
我们研究凯勒流形上格里菲斯负全形向量束总空间的凯勒度量。作为应用，我们在闭合曲面 S 的 Teichmüller 空间的全形切线束ℬ(𝒮)上构造了映射类群不变的凯勒度量，从而在准富集空间 QF(S) 上得到了一个新的映射类群不变的凯勒度量，它扩展了 Teichmüller 空间 𝒯(S)⊂QF(S)上的魏尔-彼得森度量。我们还计算了它的曲率，并证明了曲率沿同调方向的非正性。
{"title":"Curvature of new Kähler metrics on the total space of Griffiths negative vector bundle and quasi-Fuchsian space","authors":"Inkang Kim, Xueyuan Wan, Genkai Zhang","doi":"10.1142/s0219199723500591","DOIUrl":"https://doi.org/10.1142/s0219199723500591","url":null,"abstract":"<p>We study Kähler metrics on the total space of Griffiths negative holomorphic vector bundles over Kähler manifolds. As an application, we construct mapping class group invariant Kähler metrics on <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℬ</mi><mo stretchy=\"false\">(</mo><mi mathvariant=\"cal\">𝒮</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, the holomorphic tangent bundle of Teichmüller space of a closed surface <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>S</mi></math></span><span></span>. Consequently,we obtain a new mapping class group invariant Kähler metric on the quasi-Fuchsian space <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">QF</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>S</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, which extends the Weil–Petersson metric on the Teichmüller space <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">𝒯</mi><mo stretchy=\"false\">(</mo><mi>S</mi><mo stretchy=\"false\">)</mo><mo>⊂</mo><mstyle><mtext mathvariant=\"normal\">QF</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>S</mi><mo stretchy=\"false\">)</mo></math></span><span></span>. We also calculate its curvature and prove non-positivity for the curvature along the tautological directions.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072620","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 : 2024-01-24DOI: 10.1142/s0219199723500682
Nikolaos Panagiotis Souris
We study the relation between two special classes of Riemannian Lie groups with a left-invariant metric : The Einstein Lie groups, defined by the condition , and the geodesic orbit Lie groups, defined by the property that any geodesic is the integral curve of a Killing vector field. The main results imply that extensive classes of compact simple Einstein Lie groups are not geodesic orbit manifolds, thus providing large-scale answers to a relevant question of Nikonorov. Our approach involves studying and characterizing the -invariant geodesic orbit metrics on Lie groups for a wide class of subgroups that we call (weakly) regular. By-products of our work are structural and characterization results that are of independent interest for the classification problem of geodesic orbit manifolds.
我们研究了具有左不变度量 g 的两类特殊黎曼李群 G 之间的关系：由 Ricg=cg 条件定义的爱因斯坦李群和由任何大地线都是基林向量场的积分曲线这一性质定义的大地轨道李群。主要结果意味着大量紧凑简单爱因斯坦李群（G,g）不是大地轨道流形，从而为尼科诺罗夫的一个相关问题提供了大规模答案。我们的方法包括研究和表征我们称之为（弱）正则子群 K 的一大类 Lie 群 G 上的 G×K 不变大地轨道流形。我们工作的副产品是对大地轨道流形分类问题具有独立意义的结构和表征结果。
{"title":"Einstein Lie groups, geodesic orbit manifolds and regular Lie subgroups","authors":"Nikolaos Panagiotis Souris","doi":"10.1142/s0219199723500682","DOIUrl":"https://doi.org/10.1142/s0219199723500682","url":null,"abstract":"<p>We study the relation between two special classes of Riemannian Lie groups <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> with a left-invariant metric <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span>: The Einstein Lie groups, defined by the condition <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mstyle><mtext mathvariant=\"normal\">Ric</mtext></mstyle></mrow><mrow><mi>g</mi></mrow></msub><mo>=</mo><mi>c</mi><mi>g</mi></math></span><span></span>, and the geodesic orbit Lie groups, defined by the property that any geodesic is the integral curve of a Killing vector field. The main results imply that extensive classes of compact simple Einstein Lie groups <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mi>g</mi><mo stretchy=\"false\">)</mo></math></span><span></span> are not geodesic orbit manifolds, thus providing large-scale answers to a relevant question of Nikonorov. Our approach involves studying and characterizing the <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi><mo stretchy=\"false\">×</mo><mi>K</mi></math></span><span></span>-invariant geodesic orbit metrics on Lie groups <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> for a wide class of subgroups <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>K</mi></math></span><span></span> that we call (weakly) regular. By-products of our work are structural and characterization results that are of independent interest for the classification problem of geodesic orbit manifolds.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072621","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 : 2024-01-24DOI: 10.1142/s0219199723500608
Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta
In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case.
{"title":"A comparison principle for a doubly singular quasilinear anisotropic problem","authors":"Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta","doi":"10.1142/s0219199723500608","DOIUrl":"https://doi.org/10.1142/s0219199723500608","url":null,"abstract":"<p>In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator <disp-formula-group><span><math altimg=\"eq-00001.gif\" display=\"block\" overflow=\"scroll\"><mrow><mo stretchy=\"false\">−</mo><msubsup><mrow><mi mathvariant=\"normal\">Δ</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>H</mi></mrow></msubsup><mi>u</mi><mo>:</mo><mo>=</mo><mo stretchy=\"false\">−</mo><mspace width=\"-.17em\"></mspace><mo>div</mo><mo stretchy=\"false\">(</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi><mo stretchy=\"false\">−</mo><mn>1</mn></mrow></msup><mo stretchy=\"false\">(</mo><mo>∇</mo><mi>u</mi><mo stretchy=\"false\">)</mo><mo>∇</mo><mi>H</mi><mo stretchy=\"false\">(</mo><mo>∇</mo><mi>u</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo><mo>.</mo></mrow></math></span><span></span></disp-formula-group> As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072485","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号