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

 

Some basic facts on the system $ \Delta u - W_u (u) = 0$


Author: Nicholas D. Alikakos
Journal: Proc. Amer. Math. Soc. 139 (2011), 153-162
MSC (2000): Primary 35Jxx
Published electronically: July 7, 2010
MathSciNet review: 2729079
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Abstract: We rewrite the system $ \Delta u - W_u (u) = 0$, for $ u: \mathbb{R}^n \to \mathbb{R}^n$, in the form $ \operatorname{div}T = 0$, where $ T$ is an appropriate stress-energy tensor, and derive certain a priori consequences on the solutions. In particular, we point out some differences between two paradigms: the phase-transition system, with target a finite set of points, and the Ginzburg-Landau system, with target a connected manifold.


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Additional Information

Nicholas D. Alikakos
Affiliation: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece
Email: nalikako@math.uoa.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10453-7
PII: S 0002-9939(2010)10453-7
Received by editor(s): September 23, 2009
Received by editor(s) in revised form: February 20, 2010
Published electronically: July 7, 2010
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.