Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group

TL;DR

This paper proves local Lipschitz regularity for solutions to a specific orthotropic q-Laplacian-type equation in the Heisenberg group, extending regularity results to degenerate equations where only boundedness was previously known.

Contribution

It establishes Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation in the Heisenberg group, a significant advancement over known boundedness results.

Findings

Proved local Lipschitz regularity of solutions.

Extended regularity results to degenerate equations in the Heisenberg group.

Built upon and extended Zhong's work on q-Laplacian regularity.

Abstract

We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same setting and proved the H\"older regularity for the gradient of solutions. Due to the degeneracy of the current equation, such regularity for the gradient of solutions is not even known in the Euclidean setting for dimensions greater than 2, where only boundedness is expected.