p 拉普拉斯算子两相伯努利问题中的正则性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-07-16 DOI:10.1007/s00526-024-02789-3

Masoud Bayrami, Morteza Fotouhi

{"title":"p 拉普拉斯算子两相伯努利问题中的正则性","authors":"Masoud Bayrami, Morteza Fotouhi","doi":"10.1007/s00526-024-02789-3","DOIUrl":null,"url":null,"abstract":"We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to \\(C^{1,\\eta }\\) regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument. It is noteworthy that the analysis of branch points is also included.\n","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularity in the two-phase Bernoulli problem for the p-Laplace operator\",\"authors\":\"Masoud Bayrami, Morteza Fotouhi\",\"doi\":\"10.1007/s00526-024-02789-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to \\\\(C^{1,\\\\eta }\\\\) regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument. It is noteworthy that the analysis of branch points is also included.\\n\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00526-024-02789-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00526-024-02789-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明，众所周知的 ACF 函数（p-Laplacian）的任何最小值都构成了粘性解。这使得我们可以在两相自由边界点建立均匀的平坦性衰减，以提高平坦性，这归结为自由边界平坦部分的（C^{1,\eta }\ ）正则性。这一结果反过来又被用来通过二分法论证最小化的 Lipschitz 正则性。值得注意的是，分支点的分析也包括在内。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Regularity in the two-phase Bernoulli problem for the p-Laplace operator

We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to \(C^{1,\eta }\) regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument. It is noteworthy that the analysis of branch points is also included.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464