Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels
arXiv:1011.3565
Abstract
In this paper, we consider fully nonlinear integro-differential equations with possibly nonsymmetric kernels. We are able to find different versions of Alexandroff-Backelman-Pucci estimate corresponding to the full class $\cS^{\fL_0}$ of uniformly elliptic nonlinear equations with (subcritical case) and to their subclass $\cS^{\fL_0}_η$ with . We show that $\cS^{\fL_0}_η$ still includes a large number of nonlinear operators as well as linear operators. And we show a Harnack inequality, Hölder regularity, and -regularity of the solutions by obtaining decay estimates of their level sets in each cases.