Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ 1$D symmetry for solutions of semilinear and quasilinear elliptic equations


Authors: Alberto Farina and Enrico Valdinoci
Journal: Trans. Amer. Math. Soc. 363 (2011), 579-609
MSC (2010): Primary 35J92, 35J91, 35J20
Published electronically: September 21, 2010
MathSciNet review: 2728579
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Several new $ 1$D results for solutions of possibly singular or degenerate elliptic equations, inspired by a conjecture of De Giorgi, are provided. In particular, $ 1$D symmetry is proven under the assumption that either the profiles at infinity are $ 2$D, or that one level set is a complete graph, or that the solution is minimal or, more generally, $ Q$-minimal.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 35J92, 35J91, 35J20

Retrieve articles in all journals with MSC (2010): 35J92, 35J91, 35J20


Additional Information

Alberto Farina
Affiliation: Faculté des Sciences, LAMFA – CNRS UMR 6140, Université de Picardie Jules Verne, 33, rue Saint-Leu, 80039 Amiens CEDEX 1, France
Email: alberto.farina@u-picardie.fr

Enrico Valdinoci
Affiliation: Dipartimento di Matematica, Università di Roma Tor Vergata, via della ricerca scientifica, 1, I-00133 Rome, Italy
Email: enrico@mat.uniroma3.it

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05021-4
PII: S 0002-9947(2010)05021-4
Received by editor(s): April 7, 2008
Published electronically: September 21, 2010
Additional Notes: The second author was supported by MIUR Metodi variazionali ed equazioni differenziali nonlineari and FIRB Analysis and Beyond. We thank an anonymous referee whose advice improved the exposition of this paper.
Article copyright: © Copyright 2010 American Mathematical Society