article

Title: Integro-Differential equations with nonlinear directional dependence

Authors: Russell Schwab, Marcus Rang and Moritz Kassmann

Issue: Volume 63 (2014), Issue 5, 1467-1498

Abstract:

$We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [Luis \'Angel Caffarelli and Luis Silvestre, \textit{Regularity theory for fully nonlinear integro-differential equations}, Comm. Pure Appl. Math. \textbf{62} (2009), no. 5, 597--638], and are also uniform as the order of operators approaches $2$.$