论椭圆自由边界问题的非最小化解

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-05-07 DOI:10.1007/s00526-024-02739-z

Kanishka Perera

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引用次数: 0

摘要

我们提出了一个变分框架，用于研究能量不一定最小化的椭圆自由边界问题解的存在性和正则性。作为应用，我们得到了临界和次临界超线性自由边界问题的山口解，并建立了自由边界在维数\(N = 2\) 下的完全正则性和在更高维数下的部分正则性。

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On nonminimizing solutions of elliptic free boundary problems

We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and subcritical superlinear free boundary problems, and establish full regularity of the free boundary in dimension \(N = 2\) and partial regularity in higher dimensions.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464