5 papers
Interacting fronts in the strongly nonlocal Allen--Cahn equation
Erisa Hasani, Stefania Patrizi
We study the sharp-interface limit of the fractional Allen--Cahn equation in , , in the strongly nonlocal regime , for initial data consisting of fi…
The strongly nonlocal Allen-Cahn problem
Erisa Hasani, Stefania Patrizi
We study the sharp interface limit of the fractional Allen-Cahn equation $$ \varepsilon \partial_t u^{\varepsilon} = \mathcal{I}^s_n [u^{\varepsilon}] -\frac{1}{\varepsilon ^{2s}}…
A nonlinear model for long-range segregation
Howen Chuah, Stefania Patrizi, Monica Torres
We study a system of fully nonlinear elliptic equations, depending on a small parameter $\eps$, that models long-range segregation of populations. The diffusion is governed by the…
[Regularity of interfaces for a Pucci type segregation problem
Luis Caffarelli, Stefania Patrizi, Veronica Quitalo +1
We show the existence of a Lipschitz viscosity solution in to a system of fully nonlinear equations involving Pucci-type operators. We study the regularity of the interface…
On a long range segregation model
Luis A. Caffarelli, Veronica Quitalo, Stefania Patrizi
In this work we study the properties of segregation processes modeled by a family of equations where $F_i…