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 Poincaré inequality which allows us 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.
Stable Solutions of Elliptic Equations on Riemannian Manifolds / A. Farina, Y. Sire, E. Valdinoci. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 23:3(2013), pp. 1158-1172.
Stable Solutions of Elliptic Equations on Riemannian Manifolds
E. ValdinociUltimo
2013
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 Poincaré inequality which allows us 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
