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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Published electronically: July 13, 2011
MathSciNet review: 2869076
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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

Yannick Sire
Affiliation: LATP, Université Aix-Marseille 3, Marseille, France

Enrico Valdinoci
Affiliation: Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy

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.

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