arXiv subjects
Publications and source records attributed to Hector Chang-Lara.
We consider the Bernoulli one-phase free boundary problem in a domain $Ω$ and show that the free boundary $F$ is $C^{1,1/2}$ regular in a neighborhood of the fixed boundary $\partial Ω$. We achieve this by relating the behavior of $F$ near $\partial Ω$ to a Signorini-type obstacle problem.
We establish Hölder estimates for the time derivative of solutions of fully non-linear parabolic equations that does not necessarily have $C^{2,α}$ estimates.
In this paper we extend previous results on the regularity of solutions of integro-differential parabolic equations. The kernels are non necessarily symmetric which could be interpreted as a non-local drift with the same order as the diffusion. We provide an Oscillation Lemma and a Harnack Inequality which can be used to prove higher regularity estimates.