Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group
Nyckelord:
Subelliptic p-Laplacian, parabolic gradient estimates, Heisenberg groupAbstract
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.
Referera så här
Capogna, L., Citti, G., & Zhong, X. (2023). Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group. Annales Fennici Mathematici, 48(2), 411–428. https://doi.org/10.54330/afm.131227
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