For a class of competition-diffusion nonlinear systems involving the square root of the laplacian, including the fractional Gross-Pitaevskii system (Iquation Presented) we prove that L∞ boundedness implies C0,α boundedness for every α ϵ [0, 1/2), uniformly as β ← ∞. Moreover we prove that the limiting profile is C0,1/2. This system arises, for instance, in the relativistic Hartree-Fock approximation theory for k-mixtures of Bose-Einstein condensates in different hyperfine states.
Uniform Hölder bounds for strongly competing systems involving the square root of the laplacian
TERRACINI, Susanna;
2016-01-01
Abstract
For a class of competition-diffusion nonlinear systems involving the square root of the laplacian, including the fractional Gross-Pitaevskii system (Iquation Presented) we prove that L∞ boundedness implies C0,α boundedness for every α ϵ [0, 1/2), uniformly as β ← ∞. Moreover we prove that the limiting profile is C0,1/2. This system arises, for instance, in the relativistic Hartree-Fock approximation theory for k-mixtures of Bose-Einstein condensates in different hyperfine states.
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