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

Abstract

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


${\partial }_{t}u=\sum _{i=1}^{2n}{X}_i(|{\mathrm{\nabla }}_{0}u{|}^{p-2}{X}_{i}u),$


in a cylinder $\mathrm{\Omega }\times {\mathbb{R}}^{+}$, where $\mathrm{\Omega }$ is domain in the Heisenberg group ${\mathbb{H}}^n$, and $2\le p\le 4$. The result continues to hold in the more general setting of contact subRiemannian manifolds.