Some basic facts on the system $\Delta u - W_u (u) = 0$
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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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 153-162
- MSC (2000): Primary 35Jxx
- DOI: https://doi.org/10.1090/S0002-9939-2010-10453-7
- MathSciNet review: 2729079