Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition

Preprint

30 October 2008

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0810.5537

Abstract

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.

Keywords

CAFFARELLI FRIEDMAN
POSITIVE SOLUTIONS
STRONG COMPETITION
DINGER SYSTEMS
MONOTONICITY
BOUNDEDNESS
LDER BOUNDS
UNIFORM H

All Related Versions

Version 1, 2008-10-30, ArXiv

This publication has 0 references indexed in Scilit: