Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature-Reference-Cited by-同舟云学术

Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature

Published:2018-06-07 Issue:1 Volume:8 Page:1035-1042
ISSN:2191-9496
Container-title:Advances in Nonlinear Analysis
language:
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Author:

Dipierro Serena¹,Pinamonti Andrea²,Valdinoci Enrico³

Affiliation:

1. Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA-6009 Perth, Australia; and Dipartimento di Matematica “Federigo Enriques”, Università degli studi di Milano, Via Saldini 50, 20133 Milano, Italy

2. Dipartime nto di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo, Trento, Italy

3. Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA-6009 Perth, Australia; Dipartimento di Matematica “Federigo Enriques”, Università degli studi di Milano, Via Saldini 50, 20133 Milano, Italy; School of Mathematics and Statistics, University of Melbourne, Grattan Street, Parkville, VIC-3010 Melbourne, Australia; and Istituto di Matematica Applicata e Tecnologie Informatiche, Via Ferrata 1, 27100 Pavia, Italy

Abstract

Abstract We present a geometric formula of Poincaré type, which is inspired by a classical work of Sternberg and Zumbrun, and we provide a classification result of stable solutions of linear elliptic problems with nonlinear Robin conditions on Riemannian manifolds with nonnegative Ricci curvature. The result obtained here is a refinement of a result recently established by Bandle, Mastrolia, Monticelli and Punzo.

Funder

Australian Research Council

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/downloadpdf/journals/anona/8/1/article-p1035.xml

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