论文标题
海森伯格组的准椭圆形和抛物线方程的规律性理论
Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group
论文作者
论文摘要
本注释提供了有关Hölder规律性的现有文献的简洁调查，以$ $ \ sum_ {i = 1}^{2n} X_i a_i（\ nabla_0 u）= 0 A_i（\ nabla_0 U）$$在Heisenberg Group $ \ Mathbb H^n $中以$ p $ -laplacian建模，带有$ 1 \ le p <\ infty $，及其抛物线核心对应物。我们提出了一些开放问题，并概述了它们遇到的一些困难。
This note provides a succinct survey of the existing literature concerning the Hölder regularity for the gradient of weak solutions of PDEs of the form $$\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 $Ω$ 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.
