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

Mathematics in Engineering

卷:3

Luca Capogna¹  Giovanna Citti²  Nicola Garofalo³ 

[1] 1 Department of Mathematical Sciences, Worcester Polytechnic Institute, MA 01609;

[2] 2 Dipartimento di Matematica, Piazza Porta S. Donato 5, Università di Bologna, 40126 Bologna, Italy;

[3] 3 Dipartimento di Ingegneria Civile e Ambientale (DICEA), Università di Padova, 35131 Padova, Italy;

关键词: sub elliptic p-laplacian;    parabolic gradient estimates;    heisenberg group;   

DOI  :  10.3934/mine.2021008

来源: DOAJ

【 摘 要 】

We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in [31] of the Hölder regularity of $p-$harmonic functions in the Heisenberg group $\mathbb{H}^n$. Given a number $p\ge 2$, in this paper we establish the $C^{\infty}$ smoothness of weak solutions of a class of quasilinear PDE in $\mathbb{H}^n$ modeled on the equation $$∂_t u= \sum_{i=1}^{2n} X_i \bigg((1+|\nabla_0 u|^2)^{\frac{p-2}{2}} X_i u\bigg).$$

【 授权许可】

Unknown