|Titolo||Strong competition versus fractional diffusion: the case of Lotka-Volterra interaction|
|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 Lotka-Volterra type.
In the case of 2 densities we develop a quasi-optimal 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.|