Data di Pubblicazione:
2013
Citazione:
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.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Elliptic PDEs ; Riemannian manifolds ; Rigidity results
Elenco autori:
A. Farina, Y. Sire, E. Valdinoci
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