A reverse quantitative isoperimetric type inequality for the Dirichlet Laplacian

IF 0.6 4区 数学 Q3 MATHEMATICS
Gloria Paoli
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引用次数: 1

Abstract

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
Dirichlet拉普拉斯算子的一个反量化等周型不等式
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
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
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
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.
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