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

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

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...

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Bibliographic Details
Main Authors: Dipierro Serena, Pinamonti Andrea, Valdinoci Enrico
Format: Article
Language:English
Published: De Gruyter 2018-06-01
Series:Advances in Nonlinear Analysis
Subjects:
riemannian manifolds
elliptic problems
robin condition
58j05
58j32
53c24
Online Access:https://doi.org/10.1515/anona-2018-0013
Description
Summary: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.
ISSN:2191-9496
2191-950X

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