Uniform Hölder regularity with small exponent in competition-fractional diffusion systems

Abstract

For a class of competition-diffusion nonlinear systems involving fractional powers of the Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove that uniform boundedness implies Hölder boundedness for sufficiently small positive exponents, uniformly as the interspecific competition parameter diverges. This implies strong convergence of the family of solutions as the segregation of their support occurs.

arXiv commentrepeats results from arXiv:1211.6087 and generalizes to fractional powers different from the square root