极值原理的一个应用

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摘要：极值原理是抛物型方程和椭圆型方程解的重要特征之一，即方程的解的极值在区域的边界达到。本文我们运用极值原理，推出一类椭圆方程的梯度估计。

关键词：极值原理;梯度估计;椭圆型方程

DOI：10.19392/j.cnki.1671-7341.202217006

An Application of the Extremum Principle

Liang ShiyuHan FeiLuo Xiaorong

College of Mathematical Science，Xinjiang Normal UniversityXinjiangUrumqi830017

Abstract：Extremum principle is one of the important characteristics of parabolic and elliptic e-quations，that is，the extremum of the solution of the equation is reached at the boundary of the region.In this paper we derive gradient estimation for a class of elliptic equations by using extremum principle.

Keywords：extremum principle;Gradient estimation;Elliptic equation

若方程解的极值在区域的边界达到，我们称方程对应的算子满足极值原理。（剩余1220字）