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2016 $C^\sigma ,\alpha $ estimates for concave, non-local parabolic equations with critical drift
Héctor Chang Lara, Gonzalo Dávila
J. Integral Equations Applications 28(3): 373-394 (2016). DOI: 10.1216/JIE-2016-28-3-373

Abstract

Given a concave integro-differential operator $I$, we study regularity for solutions of fully nonlinear, nonlocal, parabolic 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 $C^{\sigma +\alpha }$ estimate in the spatial variable and $C^{1,\alpha }$ 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.

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Héctor Chang Lara. Gonzalo Dávila. "$C^\sigma ,\alpha $ estimates for concave, non-local parabolic equations with critical drift." J. Integral Equations Applications 28 (3) 373 - 394, 2016. https://doi.org/10.1216/JIE-2016-28-3-373

Information

Published: 2016
First available in Project Euclid: 17 October 2016

zbMATH: 1353.35083
MathSciNet: MR3562356
Digital Object Identifier: 10.1216/JIE-2016-28-3-373

Subjects:
Primary: 35B45 , 35B65 , 35D40 , 35K55 , 35R09

Keywords: Evans-Krylov estimate , fully non-linear concave operators , Non-local parabolic equations

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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