Calculus of Variations and Geometric Measure Theory
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A. Farina

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

created by farina on 20 Feb 2013

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Inserted: 20 feb 2013
Last Updated: 20 feb 2013

Year: 2013

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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