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

In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λF⁢(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 t...

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Main Authors:	Della Pietra Francesco, di Blasio Giuseppina, Gavitone Nunzia
Format:	Article
Language:	English
Published:	De Gruyter 2018-09-01
Series:	Advances in Nonlinear Analysis
Subjects:	dirichlet eigenvalues anisotropic operators optimal estimates 35p30 49q10
Online Access:	https://doi.org/10.1515/anona-2017-0281

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spelling	doaj-06bffa379ac3423398a3fd128f13e2bf2021-09-06T19:39:55ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2018-09-019127829110.1515/anona-2017-0281anona-2017-0281Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principleDella Pietra Francesco0di Blasio Giuseppina1Gavitone Nunzia2Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli studi di Napoli Federico II, Via Cintia, Monte S. Angelo – 80126Napoli, ItalyUniversità degli Studi della Campania “Luigi Vanvitelli”, viale Lincoln 5, 81100Caserta, ItalyDipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli studi di Napoli Federico II, Via Cintia, Monte S. Angelo – 80126Napoli, ItalyIn this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λF⁢(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 λF⁢(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.https://doi.org/10.1515/anona-2017-0281dirichlet eigenvaluesanisotropic operatorsoptimal estimates35p30 49q10
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Della Pietra Francesco di Blasio Giuseppina Gavitone Nunzia
spellingShingle	Della Pietra Francesco di Blasio Giuseppina Gavitone Nunzia Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle Advances in Nonlinear Analysis dirichlet eigenvalues anisotropic operators optimal estimates 35p30 49q10
author_facet	Della Pietra Francesco di Blasio Giuseppina Gavitone Nunzia
author_sort	Della Pietra Francesco
title	Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
title_short	Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
title_full	Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
title_fullStr	Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
title_full_unstemmed	Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
title_sort	sharp estimates on the first dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
publisher	De Gruyter
series	Advances in Nonlinear Analysis
issn	2191-950X
publishDate	2018-09-01
description	In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λF⁢(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 λF⁢(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.
topic	dirichlet eigenvalues anisotropic operators optimal estimates 35p30 49q10
url	https://doi.org/10.1515/anona-2017-0281
work_keys_str_mv	AT dellapietrafrancesco sharpestimatesonthefirstdirichleteigenvalueofnonlinearellipticoperatorsviamaximumprinciple AT diblasiogiuseppina sharpestimatesonthefirstdirichleteigenvalueofnonlinearellipticoperatorsviamaximumprinciple AT gavitonenunzia sharpestimatesonthefirstdirichleteigenvalueofnonlinearellipticoperatorsviamaximumprinciple
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Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

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