一类Laplace方程预定夹角问题的边界梯度估计

Gradient Estimation for a Class of Laplace Equation with Predetermined Angle Problems

研究了一类Laplace方程预定夹角问题的梯度估计,通过选取适当的辅助函数,利用函数在极大值点的性质,证明了解的内梯度估计、近边梯度估计和边界梯度估计有界.得到了一类Laplace方程中关于f依赖于x,u,Du时预定夹角的解的全局梯度估计.

In this paper,the gradient estimation of a class of predetermined Angle problems for Laplace equation was studied.By selecting an appropriate auxiliary function,the properties of the function at the maximum point were used to prove that the inner gradient estimation,the near edge gradient estimation and the boundary gradient estimation were bounded.In this paper,we obtain the global gradient estimation for the solution of a class of Laplace equation with f dependent on x,u and Du.