Calculus of Variations and Geometric Measure Theory
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A. Farina - Y. Sire - E. Valdinoci

Stable solutions of elliptic equations on riemannian manifolds

created by farina on 12 May 2011



Inserted: 12 may 2011

Year: 2008


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


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