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arXiv · 1710.07329

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

Serena Dipierro·Andrea Pinamonti·Enrico Valdinoci
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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.

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Serena Dipierro, Andrea Pinamonti, Enrico Valdinoci. 2017-10-19. Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature. https://arxiv.org/abs/1710.07329

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