Stable solutions of elliptic equations on Riemannian manifolds - Mathematics > Analysis of PDEsReportar como inadecuado




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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.



Autor: Alberto Farina, Yannick Sire, Enrico Valdinoci

Fuente: https://arxiv.org/



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