# American Institute of Mathematical Sciences

June  2014, 34(6): 2669-2691. doi: 10.3934/dcds.2014.34.2669

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

 1 Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino 2 Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano, p.za Leonardo da Vinci 32, 20133 Milano, Italy

Received  March 2013 Revised  June 2013 Published  December 2013

For a class of competition-diffusion nonlinear systems involving the $s$-power of the laplacian, $s\in(0,1)$, of the form $(-\Delta)^{s} u_i=f_i(u_i) - \beta u_i\sum_{j\neq i}a_{ij}u_j^2,\qquad i=1,\dots,k,$ we prove that $L^\infty$ boundedness implies $\mathcal{C}^{0,\alpha}$ boundedness for $\alpha>0$ sufficiently small, uniformly as $\beta\to +\infty$. This extends to the case $s\neq1/2$ part of the results obtained by the authors in the previous paper [arXiv: 1211.6087v1].
Citation: Susanna Terracini, Gianmaria Verzini, Alessandro Zilio. Uniform Hölder regularity with small exponent in competition-fractional diffusion systems. Discrete & Continuous Dynamical Systems, 2014, 34 (6) : 2669-2691. doi: 10.3934/dcds.2014.34.2669
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