C1,αC^{1,α} Interior Regularity for Nonlinear Nonlocal Elliptic Equations With Rough Kernels

preprint2013arXivOpen access

Abstract

We prove a C1,αC^{1,α} interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity of a special class of nonlinear operators.

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