Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-14 DOI:10.1007/s10957-024-02442-1

Alba Lia Masiello, Gloria Paoli

引用次数: 0

Abstract

Let \(\Omega \subset \mathbb {R}^n\) be an open, bounded and Lipschitz set. We consider the Poisson problem for the p-Laplace operator associated to \(\Omega \) with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison: we prove that the equality is achieved only if \(\Omega \) is a ball and both the solution u and the right-hand side f of the Poisson equation are radial and decreasing.

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带罗宾边界条件的 p 拉普拉斯泊松问题的刚性结果

让 \(\Omega \subset \mathbb {R}^n\) 是一个开放的、有界的和 Lipschitz 集。我们考虑与 Robin 边界条件相关的 p-Laplace 算子的泊松问题。在这种情况下，我们研究了 Talenti 型比较中的相等情况：我们证明只有当 \(\Omega \) 是一个球，并且泊松方程的解 u 和右边 f 都是径向递减时，相等才会实现。

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

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.