Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition

2009/11/16 by Benedetta Noris, Susanna Terracini, Hugo Tavares +1 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Nonlinear Photonic Systems

paper · doi:10.1002/cpa.20309

Abstract

Abstract For the positive solutions of the Gross–Pitaevskii system we prove that L ∞ ‐boundedness implies C 0,α ‐boundedness for every α ϵ (0,1), uniformly as β → +∞. Moreover, we prove that the limiting profile as β → +∞ is Lipschitz‐continuous. The proof relies upon the blowup technique and the monotonicity formulae by Almgren and Alt, Caffarelli, and 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 k > 2 densities are given. © 2009 Wiley Periodicals, Inc.

Citations

• Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames
• Variational problems with two phases and their free boundaries

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• Segregated and synchronized vector solutions to linearly coupled systems of Schrödinger equations. [europepmc]

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