Optimal in tail H\"older estimates for weak solutions of the nonlocal parabolic p-Laplace equations on the Heisenberg group

TL;DR

This paper establishes the optimal tail H"older continuity estimates for weak solutions of nonlocal parabolic p-Laplace equations on the Heisenberg group, advancing understanding of regularity in nonlocal sub-Riemannian settings.

Contribution

It introduces optimal tail conditions to prove H"older continuity for solutions on the Heisenberg group, a novel approach in nonlocal parabolic PDEs.

Findings

Proved H"older continuity under optimal tail conditions.

Extended regularity results to the Heisenberg group setting.

Provided new techniques for nonlocal PDE analysis in sub-Riemannian geometry.

Abstract

We prove the H\"older continuity for weak solutions to parabolic p-Laplace equations on the Heisenberg group. We deduce this result while considering an optimal tail condition.