$W^{\sigma ,\epsilon }$-estimates for nonlocal elliptic equations

Abstract

We prove that the fractional derivatives of solutions to a class of nonlocal fully nonlinear elliptic equations are epsilon-integrable. We follow Fanghua Lin's original approach to the analogous problem for second order 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 fractional derivatives of solutions.

14 pages

References in corpus (1)

• Regularity theory for fully nonlinear integro-differential equations

Cited by in corpus (1)

• A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity