Some elliptic PDEs on Riemannian manifolds with boundary

Yannick Sire and Enrico Valdinoci

Vol. 248 (2010), No. 2, 475–492

DOI: 10.2140/pjm.2010.248.475

Abstract

We study some rigidity properties of stable solutions of elliptic equations set on manifolds with boundary. Our results are classified by the dimension of the manifold and the sign of its Ricci curvature. As a consequence of our results on boundary reactions, we obtain several symmetry and Liouville results for nonlocal equations.

Keywords

geometric analysis, PDEs on manifolds

Mathematical Subject Classification 2000

Primary: 35B05

Milestones

Received: 24 June 2009

Revised: 8 September 2010

Accepted: 9 September 2010

Published: 1 December 2010

Proposed: Jie Qing