Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings

DOI10.1090/S0002-9939-2011-11241-3zbMath1238.58011WikidataQ115289260 ScholiaQ115289260MaRDI QIDQ2880652

Enrico Valdinoci, Alberto Farina, Yannick Sire

Publication date: 13 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

geodesicsrigidityRiemannian manifoldssemilinear elliptic partial differential equationsEuclidean universal coveringstable, bounded solutions

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semilinear elliptic equations (35J61) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53) PDEs on manifolds (35R01)

Related Items (11)

Rigidity results in diffusion Markov triples ⋮ Multiple-layer solutions to the Allen-Cahn equation on hyperbolic space ⋮ Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature ⋮ Stable solutions of symmetric systems on Riemannian manifolds ⋮ Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties ⋮ Stable solutions of symmetric systems involving hypoelliptic operators ⋮ Nonexistence of stable solutions to quasilinear elliptic equations on Riemannian manifolds ⋮ Splitting theorems on complete Riemannian manifolds with nonnegative Ricci curvature ⋮ Symmetry results for nonlinear elliptic operators with unbounded drift ⋮ Topics of stable solutions to elliptic equations ⋮ Symmetry results for stable and monotone solutions to fibered systems of PDEs

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