We investigate the rigidity properties of stable, bounded solutions of semilinear elliptic partial differential equations in Riemannian manifolds that admit a Euclidean universal covering, finding conditions under which the level sets are geodesics or the solution is constant.
Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings / A. Farina, Y. Sire, E. Valdinoci. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 140:3(2012), pp. 927-930. [10.1090/S0002-9939-2011-11241-3]
Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings
E. Valdinoci
2012
Abstract
We investigate the rigidity properties of stable, bounded solutions of semilinear elliptic partial differential equations in Riemannian manifolds that admit a Euclidean universal covering, finding conditions under which the level sets are geodesics or the solution is constant.
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