Uniform Holder bounds for strongly competing systems involving the square root of the laplacian

Susanna Terracini; Gianmaria Verzini; Alessandro Zilio

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arXiv · 1211.6087

Uniform Holder bounds for strongly competing systems involving the square root of the laplacian

Susanna Terracini·Gianmaria Verzini·Alessandro Zilio

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Abstract

For a class of competition-diffusion nonlinear systems involving the square root of the Laplacian, including the fractional Gross-Pitaevskii system, we prove that uniform boundedness implies Holder boundedness for every exponent less than 1/2, uniformly as the interspecific competition parameter diverges. Moreover we prove that the limiting profile is Holder continuous of exponent 1/2. This system arises, for instance, in the relativistic Hartree-Fock approximation theory for mixtures of Bose-Einstein condensates in different hyperfine states.

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Susanna Terracini, Gianmaria Verzini, Alessandro Zilio. 2012-11-26. Uniform Holder bounds for strongly competing systems involving the square root of the laplacian. https://arxiv.org/abs/1211.6087

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