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arXiv · 2001.08303

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

Luca Capogna·Giovanna Citti·Nicola Garofalo
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Abstract

We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in \cite{Zhong} of the H\"older regularity of $p-$harmonic functions in the Heisenberg group $\Hn$. Given a number $p\ge 2$, in this paper we establish the $C^{\infty}$ smoothness of weak solutions of quasilinear pde's in $\Hn$ modelled on the equation $$\p_t u= \sum_{i=1}^{2n} X_i \bigg((1+|\nabla_0 u|^2)^{\frac{p-2}{2}} X_i u\bigg).$$

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Luca Capogna, Giovanna Citti, Nicola Garofalo. 2020-01-22. Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group. https://arxiv.org/abs/2001.08303

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