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Archive for Rational Mechanics and Analysis

, Volume 213, Issue 1, pp 287–326 | Cite as

Monotonicity and 1-Dimensional Symmetry for Solutions of an Elliptic System Arising in Bose–Einstein Condensation

  • Alberto FarinaEmail author
  • Nicola Soave
Article

Abstract

We study monotonicity and 1-dimensional symmetry for positive solutions with algebraic growth of the following elliptic system:
$$\left\{\begin{array}{ll} -\Delta u = -u \upsilon^2 &\quad {\rm in}\, \mathbb{R}^N\\ -\Delta \upsilon= -u^2 \upsilon &\quad {{\rm in}\, \mathbb{R}^N},\end{array}\right.$$
for every dimension \({N \geqq 2}\). In particular, we prove a Gibbons-type conjecture proposed by Berestycki et al.

Keywords

Harmonic Function Linear Growth Elliptic System Einstein Condensate Entire Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.LAMFA, CNRS UMR 7352, Université de Picardie Jules VerneAmiensFrance
  2. 2.Institut Camille Jordan, CNRS UMR 5208Université Claude Bernard Lyon IVilleurbanne CedexFrance
  3. 3.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano-BicoccaMilanoItaly
  4. 4.LAMFA, CNRS UMR 7352, Université de Picardie Jules VerneAmiensFrance

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