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

We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic p-Laplacian ∂tu = 2n ∑ i=1 Xi(|∇0u| p−2 Xiu), in a cylinder Ω × R, where Ω is domain in the Heisenberg group H, and 2 ≤ p ≤ 4. The result continues to hold in the more general setting of contact sub-Riemannian manifolds.

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