Xavier Fernández‐Real

most citedSmooth approximations for fully nonlinear nonlocal elliptic equations

2 citations · 2 across the 4 of their papers we have counts for

collaborators

4 papers

math.AP2023

Generic properties in free boundary problems

Xavier Fernández-Real, Hui Yu

In this work, we show the generic uniqueness of minimizers for a large class of energies, including the Alt-Caffarelli and Alt-Phillips functionals. We then prove the generic regul…

math.AP2023

Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels

Xavier Fernández-Real, Xavier Ros-Oton

We study integro-differential elliptic equations (of order $2 s$ ) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this se…

math.AP2023★ 2 cited

Smooth approximations for fully nonlinear nonlocal elliptic equations

Xavier Fernández-Real

We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth ( $C^{\infty}$ ) solutions.

math.AP2014

Boundary regularity for the fractional heat equation

Xavier Fernández-Real, Xavier Ros-Oton

We study the regularity up to the boundary of solutions to fractional heat equation in bounded $C^{1, 1}$ domains. More precisely, we consider solutions to $\partial_t u + (-Δ)^s u=…