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arXiv · 2212.10605

Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group

Luca Capogna·Giovanna Citti·Xiao Zhong
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Abstract

This note provides a succinct survey of the existing literature concerning the H\"older regularity for the gradient of weak solutions of PDEs of the form $$\sum_{i=1}^{2n} X_i A_i(\nabla_0 u)=0 \text{ and } \partial_t u= \sum_{i=1}^{2n} X_i A_i(\nabla_0 u)$$ modeled on the $p$-Laplacian in a domain $\Omega$ in the Heisenberg group $\mathbb H^n$, with $1\le p <\infty$, and of its parabolic counterpart. We present some open problems and outline some of the difficulties they present.

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Luca Capogna, Giovanna Citti, Xiao Zhong. 2022-12-20. Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group. https://arxiv.org/abs/2212.10605

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