论文标题
进化P拉普拉斯方程的平方功能估计
Square function estimates for the evolutionary p-Laplace equation
论文作者
论文摘要
我们证明了新颖的（本地）方形函数/Carleson测量对进化$ p $ laplace方程的非阴性解决方案的估计值，在抛物线寄生虫ahlfors-david常规套件的补充中。在热方程式的情况下，拉普拉斯方程以及$ p $ laplace方程，相应的平方函数估计已证明对对称性和逆边界类型问题是基本的，尤其是在（抛物线寄生虫）统一的研究中。尽管平方函数估计的含义对进化$ p $ laplace方程的含义尚不清楚，这主要是由于缺乏同质性，但我们为抛物线均匀的重构，边界行为和FATOU型定理提供了一些初步应用，以$ \ nabla_xu $。
We prove novel (local) square function/Carleson measure estimates for non-negative solutions to the evolutionary $p$-Laplace equation in the complement of parabolic Ahlfors-David regular sets. In the case of the heat equation, the Laplace equation as well as the $p$-Laplace equation, the corresponding square function estimates have proven fundamental in symmetry and inverse/free boundary type problems, and in particular in the study of (parabolic) uniform rectifiability. Though the implications of the square function estimates are less clear for the evolutionary $p$-Laplace equation, mainly due its lack of homogeneity, we give some initial applications to parabolic uniform rectifiability, boundary behaviour and Fatou type theorems for $\nabla_Xu$.
