AN OPTIMAL POINCARE-WIRTINGER INEQUALITY IN GAUSS SPACE

被引：12

作者：

Brandolini, Barbara ^{[1
]}

Chiacchio, Francesco ^{[1
]}

Henrot, Antoine ^{[2
]}

Trombetti, Cristina ^{[1
]}

机构：

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

[2] Univ Lorraine, UMR CNRS 7502, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

来源：

MATHEMATICAL RESEARCH LETTERS | 2013年 / 20卷 / 03期

关键词：

Neumann eigenvalue; Hermite operator; sharp bounds; ISOPERIMETRIC-INEQUALITIES; NEUMANN EIGENVALUE; 1ST EIGENFUNCTION; DOMAINS; PROOF;

D O I：

10.4310/MRL.2013.v20.n3.a3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega be a smooth, convex, unbounded domain of R-N. Denote by mu(1)(Omega) the first nontrivial Neumann eigenvalue of the Hermite operator in Omega; we prove that mu(1)(Omega) >= 1. The result is sharp since equality sign is achieved when Omega is a N-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincare-Wirtinger inequality for functions belonging to the weighted Sobolev space H-1(Omega, d(gamma N)), where gamma(N) is the N-dimensional Gaussian measure.

引用

页码：449 / 457

页数：9

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