Some symmetry results for entire solutions  of an elliptic system  arising inphase separation

Alberto Farina

doi:10.3934/dcds.2014.34.2505

Article Contents

2014, Volume 34, Issue 6: 2505-2511. Doi: 10.3934/dcds.2014.34.2505

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Some symmetry results for entire solutions of an elliptic system arising in phase separation

Alberto Farina^1,

1.
LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens

Received: January 31, 2013

Revised: March 31, 2013

Published: May 2014

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Abstract

We study the one dimensional symmetry of entire solutions to an elliptic system arising in phase separation for Bose-Einstein condensates with multiple states. We prove that any monotone solution, with arbitrary algebraic growth at infinity, must be one dimensional in the case of two spatial variables. We also prove the one dimensional symmetry for half-monotone solutions, i.e., for solutions having only one monotone component.

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Mathematics Subject Classification: Primary: 35J47.

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References

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