Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle-Reference-Cited by-同舟云学术

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

Published:2018-09-20 Issue:1 Volume:9 Page:278-291
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Della Pietra Francesco¹^ORCID,di Blasio Giuseppina²,Gavitone Nunzia¹

Affiliation:

1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli” , Università degli studi di Napoli Federico II , Via Cintia, Monte S. Angelo – 80126 Napoli , Italy

2. Università degli Studi della Campania “Luigi Vanvitelli” , viale Lincoln 5, 81100 Caserta , Italy

Abstract

Abstract In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λ F ⁢ ( p , Ω )

{\lambda_{F}(p,\Omega)}

of the anisotropic p-Laplacian, 1 < p < + ∞

{1<p<+\infty}

. Our aim is to enhance, by means of the 𝒫

{\mathcal{P}}

-function method, how it is possible to get several sharp estimates for λ F ⁢ ( p , Ω )

{\lambda_{F}(p,\Omega)}

in terms of several geometric quantities associated to the domain. The 𝒫

{\mathcal{P}}

-function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

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