arXiv subjects

Hector Chang Lara

Publications and source records attributed to Hector Chang Lara.

3 recordsLinked to original sources

arXiv2014

$C^{\s+\a}$ estimates for concave, non-local parabolic equations with critical drift

Given a concave integro-differential operator $I$, we study regularity for solutions of fully nonlinear, nonlocal, parabolic, concave equations of the form $u_t-Iu=0$. The kernels are assumed to be smooth but non necessarily symmetric which accounts for a critical non-local drift. We prove a $C^{\s+\a}$ estimate in the spatial variable and a $C^{1,\a/\s}$ estimates in time assuming time regularity for the boundary data. The estimates are uniform in the order of the operator $I$, hence allowing us to extend the classical Evans-Krylov result for concave parabolic equations.

math.AP↗

arXiv2013

Free boundary on a cone

We study two phase problems posed over a two dimensional cone generated by a smooth curve $γ$ on the unit sphere. We show that when $length(γ)<2π$ the free boundary avoids the vertex of the cone. When $length(γ) \geq 2π$ we provide examples of minimizers such that the vertex belongs to the free boundary.

math.AP↗

arXiv2012

Regularity for solutions of non local, non symmetric equations

We study the regularity for solutions of fully nonlinear integro differential equations with respect to nonsymmetric kernels. More precisely, we assume that our operator is elliptic with respect to a family of integro differential linear operators where the symmetric part of the kernels have a fixed homogeneity $σ$ and the skew symmetric part have strictly smaller homogeneity $τ$. We prove a weak ABP estimate and $C^{1,α}$ regularity. Our estimates remain uniform as we take $σ\to 2$ and $τ\to 1$ so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.

math.AP↗