Cσ,αestimates for concave, non-local parabolic equations with critical drift

Héctor Chang Lara, Gonzalo Dávila

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Given a concave integro-differential opera- tor I, we study regularity for solutions of fully nonlinear, nonlocal, parabolic equations of the form ut- Iu= 0. The kernels are assumed to be smooth but non necessarily symmetric, which accounts for a critical non-local drift. We prove a C1,αestimate in the spatial variable and Cσ+αestimates 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.
Original languageEnglish
Pages (from-to)373-394
Number of pages22
JournalJournal of Integral Equations and Applications
DOIs
Publication statusPublished - 1 Jan 2016

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