Uniform Holder bounds for strongly competing systems involving the square root of the laplacian

作者：Terracini Susanna^*; Verzini Gianmaria; Zilio Alessandro

来源：Journal of the European Mathematical Society, 2016, 18(12): 2865-2924.

DOI：10.4171/JEMS/656

• Square root of the laplacian
• spatial segregation
• strongly competing systems
• optimal regularity of limiting profiles
• singular perturbations

For a class of competition-diffusion nonlinear systems involving the square root of the laplacian, including the fractional Gross-Pitaevskii system.
(-Delta)(1/2)ui = omega(!)u(i)(3) + lambda(i)u(i) - beta u(i)
[GRAPHICS]
a(ij)u(j)(2), i = 1, ... , k,
we prove that L-infinity boundedness implies C-0,C-alpha boundedness for every alpha epsilon [0, 1/ 2), uniformly as beta -> infinity. Moreover we prove that the limiting profile is C-0,C-1/2. This system arises, for instance, in the relativistic Hartree-Fock approximation theory for k-mixtures of Bose-Einstein condensates in different hyperfine states.

• 出版日期2016
• 单位中国医学科学院北京协和医院