论文标题
Heisenberg Group中一类准线性退化抛物线方程的规律性
Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group
论文作者
论文摘要
我们扩展到抛物面设置的一些想法，该想法源自Xiao Zhong在Heisenberg Group $ \ hn $中的Hölder规律性的\ cite {Zhong}中的证明。给定一个数字$ p \ ge 2 $，在本文中，我们建立了$ c^{\ infty} $弱解决方案的平滑度，以$ \ hn $模拟在等式$ \ p_t u = \ p_t u = \ sum_ = \ sum_ = \ sum_ {i = 1}^{2n}^{2n} x_i \ bigG（nabla）上u |^2）^{\ frac {p-2} {2}} x_i u \ bigg）。$$
We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in \cite{Zhong} of the Hölder regularity of $p-$harmonic functions in the Heisenberg group $\Hn$. Given a number $p\ge 2$, in this paper we establish the $C^{\infty}$ smoothness of weak solutions of quasilinear pde's in $\Hn$ modelled on the equation $$\p_t u= \sum_{i=1}^{2n} X_i \bigg((1+|\nabla_0 u|^2)^{\frac{p-2}{2}} X_i u\bigg).$$
