arXiv subjects

Gonzalo Davila

Publications and source records attributed to Gonzalo Davila.

6 recordsLinked to original sources

arXiv2016

Interior regularity for fractional systems

We study the regularity of solutions of elliptic fractional systems of order 2s, $s \in (0, 1)$, where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior Hölder estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [6] and M. Wiegner [9].

math.AP↗

arXiv2015

Dynamics of Optimal Partial Transport

This paper considers the evolution dynamics of the free boundaries in terms of the change of $m$, the allowed amount of transported mass or the change of $λ$, the transportation cost cap, i.e. the allowed maximum cost for a unit mass to be transported. Focusing on the quadratic cost function, we show Hölder and Lipschitz estimates on the speed of the free boundary motion in terms of $m$ and $λ$, respectively. It is also shown that the parameter $m$ is a Lipschitz function of $λ$, which previously was known only to be a continuous increasing function \cite{Ca-Mc}.

math.AP↗

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↗

arXiv2014

Hölder estimates for non-local parabolic equations with critical drift

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.

math.AP↗

arXiv2012

Regularity for solutions of non local parabolic equations II

We prove boundary regularity and a compactness result for parabolic nonlocal equations of the form $u_t-Iu=f$, where the operator $I$ is not necessarily translation invariant. As a consequence of this and the regularity results for translation invariant case, we obtain $C^{1,α}$ interior estimates in space for non translation invariant operators under some hypothesis on the time regularity of the boundary data.

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↗