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

Kirjoittajat

  • Luca Capogna Smith College, Department of Mathematics and Statistics
  • Giovanna Citti Università di Bologna, Dipartimento di Matematica, and Accademia dei Lincei, Centro Linceo interdisciplinare Beniamino Segre
  • Xiao Zhong University of Helsinki, Department of Mathematics and Statistics

Avainsanat:

Subelliptic p-Laplacian, parabolic gradient estimates, Heisenberg group

Abstrakti

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.

 

Osasto
Articles

Julkaistu

2023-06-22

Viittaaminen

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