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Eventual regularization of the slightly supercritical fractional Burgers equation
Chi Hin Chan, Magdalena Czubak, Luis Silvestre
We prove that a weak solution of a slightly supercritical fractional Burgers equation becomes Holder continuous for large time.
On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion
Luis Silvestre
We prove that the Hamilton Jacobi equation for an arbitrary Hamiltonian (locally Lipschitz but not necessarily convex) and fractional diffusion of order one (critical) has clas…
The Evans-Krylov theorem for non local fully non linear equations
Luis Caffarelli, Luis Silvestre
We prove an interior regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classica…
On the Evans-Krylov theorem
Luis Caffarelli, Luis Silvestre
In this note, motivated by our work on integral fully nonlinear equations, we provide a variation of the proof of Evans-Krylov theorem about the interior a priori estimat…
Regularity results for nonlocal equations by approximation
Luis Caffarelli, Luis Silvestre
In this paper we prove a nonlocal version of the Cordes-Niremberg estimates. We use it to extend our previous regularity results for fully nonlinear integro-differential equations…