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.
Citation
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
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