Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings
Authors:
Alberto Farina, Yannick Sire and Enrico Valdinoci
Journal:
Proc. Amer. Math. Soc. 140 (2012), 927-930
MSC (2010):
Primary 35J05, 58J05, 35B53, 35R01
DOI:
https://doi.org/10.1090/S0002-9939-2011-11241-3
Published electronically:
July 13, 2011
MathSciNet review:
2869076
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Alberto Farina
Affiliation:
LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, Amiens, France
Email:
alberto.farina@u-picardie.fr
Yannick Sire
Affiliation:
LATP, Université Aix-Marseille 3, Marseille, France
MR Author ID:
734674
Email:
sire@cmi.univ-mrs.fr
Enrico Valdinoci
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy
MR Author ID:
659058
Email:
enricovaldinoci@gmail.com
Received by editor(s):
December 15, 2010
Published electronically:
July 13, 2011
Additional Notes:
The third author has been supported by FIRB Analysis and Beyond.
Communicated by:
Matthew J. Gursky
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
