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

摘要

We present a geometric formula of Poincar\'e type, which is inspired by aclassical work of Sternberg and Zumbrun, and we provide a classification resultof stable solutions of linear elliptic problems with nonlinear Robin conditionson Riemannian manifolds with nonnegative Ricci curvature. The result obtained here is a refinement of a result recently established byBandle, Mastrolia, Monticelli and Punzo.