Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order

TL;DR

This paper establishes regularity estimates such as Sobolev, Harnack, and H"older inequalities for anisotropic, singular fractional orthotropic p-Laplacian operators, advancing understanding of their solutions' behavior.

Contribution

It introduces new regularity results for a class of nonlinear anisotropic fractional operators with singular kernels, including Sobolev, Harnack, and H"older estimates.

Findings

Proved a Sobolev-type inequality for the operators.

Established a weak Harnack inequality.

Derived local H"older continuity estimates.

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 H\"older estimate.