The Poisson equation involving surface measures

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2022-01-11 DOI:10.1080/03605302.2021.2013882

Marius Müller

引用次数: 2

Abstract

Abstract We prove the (optimal) -regularity of weak solutions to the equation in a domain with Dirichlet boundary conditions, where is a compact (Lipschitz) manifold and We also discuss optimality and necessity of the assumptions on Q and Γ. Our findings can be applied to study the regularity of solutions for several free boundary problems, in particular the biharmonic Alt–Caffarelli problem.

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涉及表面测度的泊松方程

摘要在紧(Lipschitz)流形的Dirichlet边界条件下，证明了方程弱解的(最优)正则性，并讨论了Q和Γ上假设的最优性和必要性。我们的发现可以应用于研究若干自由边界问题解的正则性，特别是双调和Alt-Caffarelli问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.