Laplace方程的斜导数边值问题梯度估计

The Gradient Estimation of Oblique Derivative Boundary Value Problems for Laplace Equation

本文主要是研究一类Laplace方程第二边值问题的梯度估计,通过构造合适的辅助函数,利用函数在极大值点的性质,证明Laplace方程的斜导数边值问题解的梯度估计,得到了一类带Du的Laplace方程第二类边值问题解的全局梯度估计。

In this paper, we study the gradient estimation of the second boundary value problem for a class of Laplace equations. By constructing appropriate auxiliary functions and using the properties of functions at maximum points, we prove the gradient estimation of the solution of the oblique de-rivative boundary value problem for the Laplace equation, and obtain the global gradient estima-tion of the solution of the second class boundary value problem for the Laplace equation with Du.