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

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  • 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.
    Mathematics Subject Classification: Primary: 35J47.


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    H. Berestycki, S. Terracini, K. Wang and J. Wei, On entire solutions of an elliptic system modeling phase separation, Adv. Math., 243 (2013), 102-126.doi: 10.1016/j.aim.2013.04.012.


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    B. Noris, H. Tavares, S. Terracini and G. Verzini, Uniform Holder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302.

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