Stable solutions of elliptic equations on Riemannian manifolds
Farina, Alberto ; Sire, Yannick ; Valdinoci, Enrico
arXiv, 0809.3025 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2008-09-17
Classification:  Mathematics - Analysis of PDEs 
@article{0809.3025,
     author = {Farina, Alberto and Sire, Yannick and Valdinoci, Enrico},
     title = {Stable solutions of elliptic equations on Riemannian manifolds},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0809.3025}
}

Farina, Alberto; Sire, Yannick; Valdinoci, Enrico. Stable solutions of elliptic equations on Riemannian manifolds. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0809.3025/