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 $$\p_t u= \sum_{i=1}^{2n} X_i (|\nabla_0 u|^{p-2} X_i u),$$ in a cylinder $\Omega \times {\mathbb{R}}^{+}$, where $\Omega$ is domain in the Heisenberg group $\Hn$, and $2\le p\le 4$. The result continues to hold in the more general setting of contact sub-Riemannian manifolds.

References in corpus (1)

• Regularity for variational problems in the Heisenberg group