The equality case in a Poincare-Wirtinger type inequality

被引：3

作者：

Brandolini, Barbara ^{[1
]}

Chiacchio, Francesco ^{[1
]}

Krejcirik, David ^{[2
]}

Trombetti, Cristina ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Complesso Monte S Angelo,Via Cintia, I-80126 Naples, Italy

[2] Acad Sci Czech Republic, Inst Nucl Phys, Dept Theoret Phys, Rez, Czech Republic

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2016年 / 27卷 / 04期

关键词：

Hermite operator; Neumann eigenvalues; thin strips; ISOPERIMETRIC-INEQUALITIES; NEUMANN EIGENVALUE; CONVEX DOMAINS; GAUSS SPACE; PERTURBATIONS;

D O I：

10.4171/RLM/743

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that, for any convex planar set Omega, the first non-trivial Neumann eigenvalue mu(1)(Omega) of the Hermite operator is greater than or equal to 1. Under the additional assumption that W is contained in a strip, we show that mu(1)(Omega) = 1 if and only if W is any strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.

引用

页码：443 / 464

页数：22

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