数学物理方程中的极值原理——具有斜导数边界条件的椭圆方程

The Maximum Principles of Differential Equations in Mathematical Physics—Elliptic Equations with Oblique Derivative Boundary Condition

极值原理则是研究椭圆型偏微分方程的重要工具之一。椭圆方程的极值原理多数情况下都是在狄利克雷边界条件下得出的。本文在此基础上,首先对斜导数边界进行了说明,接着又对一般情形的极值原理进行简单概括,最后得出了带有斜导数边界条件椭圆方程的极值原理。

The maximum principle is one of the important tools for studying elliptic partial differential equations. In most situations, the maximum principle is derived under the Dirichlet boundary conditions. This paper considers the oblique derivative boundary conditions. Firstly, we explain the oblique derivative boundary. Then the general maximum principle is introduced. Finally, we obtain the maximum principle with the oblique derivative boundary condition for elliptic.