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

2021/06/10 by Luca Capogna, Capogna, Luca, Giovanna Citti +3 · 1 citation
Computer Science · Mathematics · #35H20 #35K65 #35K92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2106.05998

openalex publication_date 2021/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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= ∑_i=1²ⁿ X_i (|∇₀ u|^p-2 X_i u), in a cylinder Ω× \R⁺, where Ω is domain in the Heisenberg group \Hn, and 2≤ p ≤ 4. The result continues to hold in the more general setting of contact sub-Riemannian manifolds.

Citations

• Regularity for variational problems in the Heisenberg group

Cited by

• Gradient estimates for an orthotropic nonlinear diffusion equation in the Heisenberg group

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