極值原理的一個應用

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摘要：極值原理是拋物型方程和橢圓型方程解的重要特征之一，即方程的解的極值在區(qū)域的邊界達到。本文我們運用極值原理，推出一類橢圓方程的梯度估計。

關鍵詞：極值原理;梯度估計;橢圓型方程

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

若方程解的極值在區(qū)域的邊界達到，我們稱方程對應的算子滿足極值原理。（剩余1220字）