Sharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators

被引：36

作者：

Della Pietra, Francesco ^{[1
]}

Gavitone, Nunzia ^{[2
]}

机构：

[1] Univ Molise, Dipartimento Biosci & Terr, Div Fis Informat & Matemat, I-86039 Termoli, CB, Italy

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

来源：

MATHEMATISCHE NACHRICHTEN | 2014年 / 287卷 / 2-3期

关键词：

Eigenvalue problems; torsional rigidity; anisotropic operators; stability estimates; POLYA-SZEGO INEQUALITY; CONVEX SYMMETRIZATION; WULFF THEOREM; P-LAPLACIAN; QUESTIONS;

D O I：

10.1002/mana.201200296

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the operator Delta(p)u = Sigma i partial derivative/partial derivative x(i) (vertical bar Delta u vertical bar(p-2) partial derivative u/partial derivative x(i)), that is the p-Laplacian, and (Delta) over tilde (p)u = Sigma i partial derivative/partial derivative x(i) (vertical bar partial derivative u/partial derivative x(i)vertical bar(p-2) partial derivative u/partial derivative x(i)), namely the pseudo-p-Laplacian. Moreover we prove a stability result by means of a suitable isoperimetric deficit. Finally, we give a sharp lower bound for the anisotropic p-torsional rigidity. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：194 / 209

页数：16

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