Regularity for Fully Nonlinear Integro-differential Operators with Regularly Varying Kernels

摘要

In this paper, the regularity results for the integro-differential operators of the fractional Laplacian type by Caffarelli and Silvestre (Comm. Pure Appl. Math. 62, 597-638, 2009) are extended to those for the integro-differential operators associated with symmetric, regularly varying kernels at zero. In particular, we obtain the uniform Harnack inequality and Holder estimate of viscosity solutions to the nonlinear integro-differential equations associated with the kernels K-sigma,K-beta satisfying