Dirichlet拉普拉斯算子的一个反量化等周型不等式

IF 0.6 4区数学 Q3 MATHEMATICS

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-05-07 DOI:10.4171/rlm/973

Gloria Paoli

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引用次数: 1

摘要

对于拉普拉斯算子的第一个狄利克雷特征值，得到了关于周长的稳定性结果。特别地，我们证明了，一旦我们固定了维数nŞ2，就存在一个仅依赖于n的常数cã0，使得对于每一个体积等于半径为1的球B的体积的ΩĂR开、有界和凸集，它保持λ1pΩq́。本文的炉膛是对Fraenkel不对称周长的一个尖锐估计。MSC 2020:35J05，35J57，52A27

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A reverse quantitative isoperimetric type inequality for the Dirichlet Laplacian

A stability result in terms of the perimeter is obtained for the first Dirichlet eigenvalue of the Laplacian operator. In particular, we prove that, once we fix the dimension n ě 2, there exists a constant c ą 0, depending only on n, such that, for every Ω Ă R open, bounded and convex set with volume equal to the volume of a ball B with radius 1, it holds λ1pΩq ́ λ1pBq ě c pP pΩq ́ P pBqq , where by λ1p ̈q we denote the first Dirichlet eigenvalue of a set and by P p ̈q its perimeter. The hearth of the present paper is a sharp estimate of the Fraenkel asymmetry in terms of the perimeter. MSC 2020: 35J05, 35J57, 52A27

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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.