Geodesic
Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group
Luca Capogna1 ; Giovanna Citti2 ; Xiao Zhong3
1Smith College, Department of Mathematics and Statistics
2Università di Bologna, Dipartimento di Matematica, and Accademia dei Lincei, Centro Linceo interdisciplinare Beniamino Segre
3University of Helsinki, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 411-428

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We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic $p$-Laplacian $\partial_t u= \sum_{i=1}^{2n} X_i (|\nabla_0 u|^{p-2} X_i u),$in a cylinder $\Omega\times\mathbb{R}^+$, where $\Omega$ is domain in the Heisenberg group $\mathbb{H}^n$, and $2\le p \le 4$. The result continues to hold in the more general setting of contact subRiemannian manifolds.  
DOI : 10.54330/afm.131227
Keywords: Subelliptic p-Laplacian, parabolic gradient estimates, Heisenberg group

Luca Capogna  1   ; Giovanna Citti  2   ; Xiao Zhong  3

1 Smith College, Department of Mathematics and Statistics
2 Università di Bologna, Dipartimento di Matematica, and Accademia dei Lincei, Centro Linceo interdisciplinare Beniamino Segre
3 University of Helsinki, Department of Mathematics and Statistics 
Luca Capogna; Giovanna Citti; Xiao Zhong. Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 411-428. doi: 10.54330/afm.131227
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