具有Robin边界条件的扭转函数的一些性质

IF 0.6 4区数学 Q3 MATHEMATICS

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2020-10-15 DOI:10.4171/rlm/962

Rossano Sannipoli

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引用次数: 2

摘要

本文研究了具有Robin边界条件的扭转函数的一些性质。在这里，我们给出了扭转函数的$L^和$L^p$范数的形状导数，对于$p\ge1$，扭转函数被视为有界单连通域$\Omega\in\mathbb｛R｝^n$上的函数，并证明了当体积保持时，球是这些泛函的临界形状。

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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Some properties of the torsion function with Robin boundary conditions

In this paper we study some properties of the torsion function with Robin boundary conditions. Here we write the shape derivative of the $L^{\infty}$ and $L^p$ norms, for $p\ge 1$, of the torsion function, seen as a functional on a bounded simply connected domain $\Omega \in \mathbb{R}^n$, and prove that the balls are a critical shape for these functionals, when the volume is preserved.

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来源期刊

Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.