Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group

2020/01/22 by Capogna, Luca, Citti, Giovanna, Garofalo, Nicola
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.08303

Abstract

We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in \citeZhong of the Hölder regularity of p-harmonic functions in the Heisenberg group \Hn. Given a number p≥ 2, in this paper we establish the C^∞ smoothness of weak solutions of quasilinear pde's in \Hn modelled on the equation \p_t u= ∑_i=1²ⁿ X_i ((1+|∇₀ u|²)^(p-2)/(2) X_i u).

Related

• Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group
• Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group
• C^1,α-Regularity of Quasilinear equations on the Heisenberg Group
• Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail
• On the C^1,α Regularity of p-Harmonic Functions in the Heisenberg Group