Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-04 DOI:10.1515/acv-2023-0005

Iwona Chlebicka, Flavia Giannetti, Anna Zatorska-Goldstein

{"title":"Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data","authors":"Iwona Chlebicka, Flavia Giannetti, Anna Zatorska-Goldstein","doi":"10.1515/acv-2023-0005","DOIUrl":null,"url":null,"abstract":"Abstract We establish pointwise bounds expressed in terms of a nonlinear potential of a generalized Wolff type for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">𝒜</m:mi> </m:math> {{\\mathcal{A}}} -superharmonic functions with nonlinear operator <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"script\">𝒜</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>×</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> <m:mo>→</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> </m:mrow> </m:math> {{\\mathcal{A}}:\\Omega\\times{\\mathbb{R}^{n}}\\to{\\mathbb{R}^{n}}} having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls estimates from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfy conditions expressed in the natural scales. Finally, we give a variant of Hedberg–Wolff theorem on characterization of the dual of the Orlicz space.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/acv-2023-0005","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

Abstract We establish pointwise bounds expressed in terms of a nonlinear potential of a generalized Wolff type for 𝒜 {{\mathcal{A}}} -superharmonic functions with nonlinear operator 𝒜 : Ω × ℝ n → ℝ n {{\mathcal{A}}:\Omega\times{\mathbb{R}^{n}}\to{\mathbb{R}^{n}}} having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls estimates from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfy conditions expressed in the natural scales. Finally, we give a variant of Hedberg–Wolff theorem on characterization of the dual of the Orlicz space.

查看原文本刊更多论文

具有Orlicz增长和测量数据的椭圆型问题解的Wolff势和局部行为

我们建立了用广义Wolff型的非线性势表示的点边界，即具有非线性算子的{\mathcal{a}} -超调和函数:Ω x∈n→∈{\mathcal{a}}:\ Ω \乘以{\mathbb{R}^{n}}到{\mathbb{R}^{n}}}，对空间变量和最后一个变量的Orlicz增长具有可测量的依赖关系。结果是尖锐的，因为相同的潜在控制从上面和从下面估计。应用它，我们提供了一系列精确的规律性结果，包括连续性和Hölder连续性，用于解决涉及满足自然尺度表示的条件的措施的问题。最后，我们给出了关于Orlicz空间对偶性质的Hedberg-Wolff定理的一个变体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.