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

Dennis Kriventsov

paper

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

arXiv:1304.7525

Abstract

We prove a $C^{1, α}$ 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.

23 pages, submitted, Communications in PDE

C1,α Interior Regularity for Nonlinear Nonlocal Elliptic Equations With Rough Kernels

Abstract

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