Codice  QDD 162 
Titolo  Strong competition versus fractional diffusion: the case of LotkaVolterra interaction 
Data  20131030 
Autore/i  Verzini, G.; Zilio, A. 
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Abstract  We consider a system of differential equations with nonlinear Steklov boundary conditions, related to a stationary problem for many densities subject to fractional diffusion and strong competition of LotkaVolterra type.
In the case of 2 densities we develop a quasioptimal regularity theory in
Holder spaces of any exponent less than the optimal one, uniformly w.r.t. the competition parameter. Moreover we show that the traces of the limiting
profiles (as the competition parameter goes to infinity) are Lipschitz continuous and segregated.
Such results are extended to the case of 3 or more densities, with some restrictions on the parameters of the system.
Since for competition of variational type the optimal regularity is known to be lower, these results mark a substantial difference with the case of standard diffusion, where the two competitions can not be distinguished from each other in the limit. 
