Stable solutions of elliptic equations on Riemannian manifolds - Mathematics > Analysis of PDEsReport as inadecuate




Stable solutions of elliptic equations on Riemannian manifolds - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: This paper is devoted to the study of rigidity properties for specialsolutions of nonlinear elliptic partial differential equations on smooth,boundaryless Riemannian manifolds. As far as stable solutions are concerned, wederive a new weighted Poincar\-e inequality which allows to prove Liouvilletype results and the flatness of the level sets of the solution in dimension 2,under suitable geometric assumptions on the ambient manifold.



Author: Alberto Farina, Yannick Sire, Enrico Valdinoci

Source: https://arxiv.org/







Related documents