{"title":"具有边界双相增长的渐近凸泛函的部分Hölder正则性","authors":"Wenrui Chang, Shenzhou Zheng","doi":"10.1002/mana.202400388","DOIUrl":null,"url":null,"abstract":"<p>We study partial Hölder regularity of the local minimizers <span></span><math>\n <semantics>\n <mrow>\n <mi>u</mi>\n <mo>∈</mo>\n <msubsup>\n <mi>W</mi>\n <mi>loc</mi>\n <mrow>\n <mn>1</mn>\n <mo>,</mo>\n <mn>1</mn>\n </mrow>\n </msubsup>\n <mrow>\n <mo>(</mo>\n <mi>Ω</mi>\n <mo>;</mo>\n <msup>\n <mi>R</mi>\n <mi>N</mi>\n </msup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$u\\in W_{\\mathrm{loc}}^{1,1}(\\Omega;{\\mathbb {R}^N})$</annotation>\n </semantics></math> with <span></span><math>\n <semantics>\n <mrow>\n <mi>N</mi>\n <mo>≥</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$N\\ge 1$</annotation>\n </semantics></math> to the integral functional <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mo>∫</mo>\n <mi>Ω</mi>\n </msub>\n <mi>F</mi>\n <mrow>\n <mo>(</mo>\n <mi>x</mi>\n <mo>,</mo>\n <mi>u</mi>\n <mo>,</mo>\n <mi>D</mi>\n <mi>u</mi>\n <mo>)</mo>\n </mrow>\n <mspace></mspace>\n <mi>d</mi>\n <mi>x</mi>\n </mrow>\n <annotation>$\\int _\\Omega F(x,u,Du)\\,dx$</annotation>\n </semantics></math> in a bounded domain <span></span><math>\n <semantics>\n <mrow>\n <mi>Ω</mi>\n <mo>⊂</mo>\n <msup>\n <mi>R</mi>\n <mi>n</mi>\n </msup>\n </mrow>\n <annotation>$\\Omega \\subset \\mathbb {R}^n$</annotation>\n </semantics></math> for <span></span><math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>≥</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$n\\ge 2$</annotation>\n </semantics></math>. Under the assumption of asymptotically convex to the borderline double-phase functional\n\n </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1018-1040"},"PeriodicalIF":0.8000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partial Hölder regularity for asymptotically convex functionals with borderline double-phase growth\",\"authors\":\"Wenrui Chang, Shenzhou Zheng\",\"doi\":\"10.1002/mana.202400388\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study partial Hölder regularity of the local minimizers <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>u</mi>\\n <mo>∈</mo>\\n <msubsup>\\n <mi>W</mi>\\n <mi>loc</mi>\\n <mrow>\\n <mn>1</mn>\\n <mo>,</mo>\\n <mn>1</mn>\\n </mrow>\\n </msubsup>\\n <mrow>\\n <mo>(</mo>\\n <mi>Ω</mi>\\n <mo>;</mo>\\n <msup>\\n <mi>R</mi>\\n <mi>N</mi>\\n </msup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$u\\\\in W_{\\\\mathrm{loc}}^{1,1}(\\\\Omega;{\\\\mathbb {R}^N})$</annotation>\\n </semantics></math> with <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>N</mi>\\n <mo>≥</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$N\\\\ge 1$</annotation>\\n </semantics></math> to the integral functional <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mo>∫</mo>\\n <mi>Ω</mi>\\n </msub>\\n <mi>F</mi>\\n <mrow>\\n <mo>(</mo>\\n <mi>x</mi>\\n <mo>,</mo>\\n <mi>u</mi>\\n <mo>,</mo>\\n <mi>D</mi>\\n <mi>u</mi>\\n <mo>)</mo>\\n </mrow>\\n <mspace></mspace>\\n <mi>d</mi>\\n <mi>x</mi>\\n </mrow>\\n <annotation>$\\\\int _\\\\Omega F(x,u,Du)\\\\,dx$</annotation>\\n </semantics></math> in a bounded domain <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>Ω</mi>\\n <mo>⊂</mo>\\n <msup>\\n <mi>R</mi>\\n <mi>n</mi>\\n </msup>\\n </mrow>\\n <annotation>$\\\\Omega \\\\subset \\\\mathbb {R}^n$</annotation>\\n </semantics></math> for <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>n</mi>\\n <mo>≥</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$n\\\\ge 2$</annotation>\\n </semantics></math>. Under the assumption of asymptotically convex to the borderline double-phase functional\\n\\n </p>\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"298 3\",\"pages\":\"1018-1040\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-02-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400388\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400388","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了局部最小值 u∈ W loc 1 , 1 ( Ω ; R N ) $u\in W_{mathrm{loc}}^{1,1}(\Omega;{\mathbb {R}^N})$ N ≥ 1 $N\ge 1$ 的积分函数∫ Ω F ( x , u , D u ) d x $\int _\Omega F(x,u,Du)\,dx$ 在 n ≥ 2 $n\ge 2$ 的有界域 Ω ⊂ R n $\Omega \子集 \mathbb {R}^n$ 中的部分赫尔德正则性。在近似凸向边界双相函数的假设下
Partial Hölder regularity for asymptotically convex functionals with borderline double-phase growth
We study partial Hölder regularity of the local minimizers with to the integral functional in a bounded domain for . Under the assumption of asymptotically convex to the borderline double-phase functional
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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