Wσ,ϵ-estimates for nonlocal elliptic equations

Abstract

We prove a $W^{\sigma ,ϵ}$-estimate for a class of nonlocal fully nonlinear elliptic equations by following Fanghua Lin's original approach [8] to the analogous problem for second order elliptic equations, by first proving a potential estimate, then combining this estimate with the ABP-type estimate by N. Guillen and R. Schwab to control the size of the superlevel sets of the σ-order derivatives of solutions.