Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

被引：22
作者：
Della Pietra, Francesco [1 ]
Di Blasio, Giuseppina [2 ]
Gavitone, Nunzia [1 ]
机构：
[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia, I-80126 Naples, Italy
[2] Univ Campania Luigi Vanvitelli, Viale Lincoln 5, I-81100 Caserta, Italy
来源：
ADVANCES IN NONLINEAR ANALYSIS | 2020年 / 9卷 / 01期
关键词：
Dirichlet eigenvalues; anisotropic operators; optimal estimates; TORSIONAL RIGIDITY; BOUNDS; INEQUALITY; SETS;
D O I：
10.1515/anona-2017-0281
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue lambda(F) (p, Omega) of the anisotropic p-Laplacian, 1 < p < +infinity. Our aim is to enhance, by means of the P-function method, how it is possible to get several sharp estimates for lambda(F)(p, Omega) in terms of several geometric quantities associated to the domain. The P-function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient.
引用
收藏
页码：278 / 291
页数：14
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