Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition |
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| Authors: | Benedetta Noris Susanna Terracini Hugo Tavares Gianmaria Verzini |
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| Institution: | 1. Università degli Studi di Milano‐Bicocca, Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy;2. Universidade de Lisboa, Faculdade de Ciências, CMAF, Avenida Professor Gama Pinto, 2, 1649‐003 Lisbon, Portugal;3. Politecnico di Milano, Dipartimento di Matematica, p.za Leonardo da Vinci 32, 20133 Milan, Italy |
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| Abstract: | For the positive solutions of the Gross–Pitaevskii system  we prove that L∞‐boundedness implies C0,α‐boundedness for every α ? (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. |
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