Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group

Authors

  • Luca Capogna Smith College, Department of Mathematics and Statistics
  • Giovanna Citti Università di Bologna, Dipartimento di Matematica, and Accademia dei Lincei, Centro Linceo interdisciplinare Beniamino Segre
  • Xiao Zhong University of Helsinki, Department of Mathematics and Statistics

Keywords:

Subelliptic p-Laplacian, parabolic gradient estimates, Heisenberg group

Abstract

We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic p-Laplacian


tu=i=12nXi(|0u|p2Xiu),


in a cylinder Ω×R+, where Ω is domain in the Heisenberg group Hn, and 2p4. The result continues to hold in the more general setting of contact subRiemannian manifolds.

 

Section
Articles

Published

2023-06-22

How to Cite

Capogna, L., Citti, G., & Zhong, X. (2023). Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group. Annales Fennici Mathematici, 48(2), 411–428. https://doi.org/10.54330/afm.131227