Uniform H\"older regularity with small exponent in competition-fractional diffusion systems
Analysis of PDEs
2013-04-02 v1
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 H\"older 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.
Cite
@article{arxiv.1303.6079,
title = {Uniform H\"older regularity with small exponent in competition-fractional diffusion systems},
author = {Susanna Terracini and Gianmaria Verzini and Alessandro Zilio},
journal= {arXiv preprint arXiv:1303.6079},
year = {2013}
}
Comments
repeats results from arXiv:1211.6087 and generalizes to fractional powers different from the square root