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math.AP2025
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}}…
math.AP2025
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…
math.AP2018
[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…