Regularity estimates for fractional orthotropic p-Laplacians of mixed order

Abstract

We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequality, a weak Harnack inequality, and a local Hölder estimate.

Keywords

• nonlocal operators
• divergence form
• regularity theory
• anisotropic measures
• weak harnack inequality
• 35b65
• 47g20
• 31b05
• 42b25