naa a22 4500 510810667 CHVBK 20180411083441.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9278-9 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9278-9 Stable Solutions of Elliptic Equations on Riemannian Manifolds [Elektronische Daten] [Alberto Farina, Yannick Sire, Enrico Valdinoci] 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. Mathematica Josephina, Inc., 2011 Elliptic PDEs nationallicence Riemannian manifolds nationallicence Rigidity results nationallicence Farina Alberto Faculté des Sciences, LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, 33, rue Saint-Leu, Amiens, France aut Sire Yannick Paul Cézanne, LATP, Université Aix-Marseille 3, Cour A, Bat. Poincare, Avenue Escadrille Normandie-Niemen 13397, Marseille, France aut Valdinoci Enrico Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, Milan, Italy aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1158-1172 1050-6926 23:3<1158 2013 23 12220 https://doi.org/10.1007/s12220-011-9278-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9278-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farina Alberto Faculté des Sciences, LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, 33, rue Saint-Leu, Amiens, France aut NATIONALLICENCE 700 1- Sire Yannick Paul Cézanne, LATP, Université Aix-Marseille 3, Cour A, Bat. Poincare, Avenue Escadrille Normandie-Niemen 13397, Marseille, France aut NATIONALLICENCE 700 1- Valdinoci Enrico Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, Milan, Italy aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1158-1172 1050-6926 23:3<1158 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer