English

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

Analysis of PDEs 2026-01-21 v3

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.

Keywords

Cite

@article{arxiv.2407.07548,
  title  = {Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group},
  author = {Michele Circelli and Giovanna Citti and Albert Clop},
  journal= {arXiv preprint arXiv:2407.07548},
  year   = {2026}
}