Uniform H\"older regularity with small exponent in competition-fractional diffusion systems

Susanna Terracini; Gianmaria Verzini; Alessandro Zilio

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arXiv · 1303.6079

Uniform H\"older regularity with small exponent in competition-fractional diffusion systems

Susanna Terracini·Gianmaria Verzini·Alessandro Zilio

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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.

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Susanna Terracini, Gianmaria Verzini, Alessandro Zilio. 2013-03-25. Uniform H\"older regularity with small exponent in competition-fractional diffusion systems. https://arxiv.org/abs/1303.6079

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