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

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4 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 languageEnglish
JournalAdvances in Nonlinear Analysis
DOIs
Publication statusE-pub ahead of print - 7 Jun 2018

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Nonnegative Curvature
Stable Solution
Ricci Curvature
Nonlinear Boundary Conditions
Riemannian Manifold
Boundary Value Problem
Elliptic Problems
Refinement

Cite this

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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",
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AU - Pinamonti, A.

AU - Valdinoci, E.

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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

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JO - Advances in Nonlinear Analysis

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SN - 2191-9496

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