Regularity for a Class of Quasilinear Degenerate Parabolic Equations in the Heisenberg Group

Authors

Luca Capogna, Worcester Polytechnic InstituteFollow
Giovanna Citti, Alma Mater Studiorum Università di Bologna
Nicola Garofalo, Università degli Studi di Padova

Document Type

Article

Publication Date

1-1-2021

Publication Title

Mathematics In Engineering

Abstract

We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in [31] of the Hölder regularity of p-harmonic functions in the Heisenberg group Hn. Given a number p ≥ 2, in this paper we establish the C1 smoothness of weak solutions of a class of quasilinear PDE in Hn modeled on the equation.

Keywords

Heisenberg group, Parabolic gradient estimates, Sub elliptic p-Laplacian

Volume

3

Issue

1

First Page

1

Last Page

31

DOI

10.3934/mine.2021008

Comments

Author’s submitted manuscript.

Recommended Citation

Capogna, Luca; Citti, Giovanna; and Garofalo, Nicola, "Regularity for a Class of Quasilinear Degenerate Parabolic Equations in the Heisenberg Group" (2021). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/124