Free boundary partial regularity in the thin obstacle problem

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-09-05 DOI:10.1002/cpa.22152

Federico Franceschini, Joaquim Serra

{"title":"Free boundary partial regularity in the thin obstacle problem","authors":"Federico Franceschini, Joaquim Serra","doi":"10.1002/cpa.22152","DOIUrl":null,"url":null,"abstract":"For the thin obstacle problem in <math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mi>n</mi>\n </msup>\n <annotation>$\\mathbb {R}^n$</annotation>\n </semantics></math>, <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>, we prove that at all free boundary points, with the exception of a <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>n</mi>\n <mo>−</mo>\n <mn>3</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$(n-3)$</annotation>\n </semantics></math>-dimensional set, the solution differs from its blow-up by higher order corrections. This expansion entails a C1, 1-type free boundary regularity result, up to a codimension 3 set.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 1","pages":"630-669"},"PeriodicalIF":3.1000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22152","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

Abstract

For the thin obstacle problem in $R^{n}$ , $n \geq 2$ , we prove that at all free boundary points, with the exception of a $(n - 3)$ -dimensional set, the solution differs from its blow-up by higher order corrections. This expansion entails a C^{1, 1}-type free boundary regularity result, up to a codimension 3 set.

查看原文本刊更多论文

薄障碍问题的自由边界部分正则性

对于中的薄障碍问题，我们证明了在所有自由边界点，除了一个维度集，该解与它的爆破不同于高阶修正。这种展开需要C1，1型自由边界正则性结果，直到余维3集合。

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

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.