Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-10-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2021008/fulltext.html |
| Summary: | 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 $$∂_t u= \sum_{i=1}^{2n} X_i \bigg((1+|\nabla_0 u|^2)^{\frac{p-2}{2}} X_i u\bigg).$$ |
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| ISSN: | 2640-3501 |