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

S. Dipierro; A. Pinamonti; E. Valdinoci

doi:10.1515/anona-2018-0013

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

S. Dipierro, A. Pinamonti, E. Valdinoci

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article

8 Citations (Scopus)

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.

Original language	English
Journal	Advances in Nonlinear Analysis
DOIs	https://doi.org/10.1515/anona-2018-0013
Publication status	E-pub ahead of print - 7 Jun 2018

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

abstract = "We present a geometric formula of Poincar{\'e} 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.",

author = "S. Dipierro and A. Pinamonti and E. Valdinoci",

year = "2018",

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AU - Dipierro, S.

AU - Pinamonti, A.

AU - Valdinoci, E.

PY - 2018/6/7

Y1 - 2018/6/7

N2 - 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.

AB - 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.

U2 - 10.1515/anona-2018-0013

DO - 10.1515/anona-2018-0013

M3 - Article

JO - Advances in Nonlinear Analysis

JF - Advances in Nonlinear Analysis

SN - 2191-9496

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