Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition

Details Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition

2008-10-30

arxiv.org/abs/0810.5537v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

For the positive solutions of the competitive Gross-Pitaevskii system of two equations, we prove that L^\infty boundedness implies uniform H\"older boundedness as the competition parameter goes to infinity. Moreover we prove that the limiting profile is Lipschitz continuous. The proof relies upon the blow-up technique and the monotonicity formulae by Almgren and Alt-Caffarelli-Friedman. This system arises in the Hartree-Fock approximation theory for binary mixtures of Bose-Einstein condensates in different hyperfine states. Extensions to systems with more than two densities are given.

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