5 citations · 7 across the 5 of their papers we have counts for
11 papers
Bellman Equations with Sub-Lipschitz Hessians
Xavier Fernández-Real
We construct homogeneous solutions with non-Lipschitz Hessian for finite, constant-coefficient Bellman equations. First, for every , we find two uniformly elliptic matri…
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…
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 ) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this se…
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 () solutions.
Infinite-width limit of deep linear neural networks
Lénaïc Chizat, Maria Colombo, Xavier Fernández-Real +1
This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dyn…
Improved regularity of second derivatives for subharmonic functions
Xavier Fernández-Real, Riccardo Tione
In this note, we prove that if a subharmonic function has pure second derivatives that are signed measures, then their negative part $(\partial_{ii} u)_…