Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings
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- by Alberto Farina, Yannick Sire and Enrico Valdinoci PDF
- Proc. Amer. Math. Soc. 140 (2012), 927-930 Request permission
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.References
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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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2869076