Uniform Holder Bounds for Nonlinear Schrodinger Systems with Strong Competition

被引：210

作者：

Noris, Benedetta ^{[1
]}

Tavares, Hugo ^{[2
]}

Terracini, Susanna ^{[1
]}

Verzini, Gianmaria ^{[3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20126 Milan, Italy

[2] Univ Lisbon, Fac Ciencias, CMAF, P-1649003 Lisbon, Portugal

[3] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2010年 / 63卷 / 03期

关键词：

ELLIPTIC-SYSTEMS; SPATIAL SEGREGATION; FREE-BOUNDARIES; EQUATIONS; PHASES; WAVES;

D O I：

10.1002/cpa.20309

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the positive solutions of the Gross-Pitaevskii system [GRAPHICS] we prove that L(infinity)-boundedness implies C(0,alpha)-boundedness for every alpha is an element of (0, 1), uniformly as beta -> +infinity. Moreover, we prove that the limiting profile as beta -> +infinity 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. (C) 2009 Wiley Periodicals, Inc.

引用

页码：267 / 302

页数：36

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