一类拟线性椭圆方程的强解的存在性  

The Existence of a Strong Solution for a Class of Quasi-linear Elliptic Equations

作　　者：邢健儒 罗宏[2] 

机构地区：[1]四川大学数学学院,四川成都610068 [2]四川大学数学与软件科学学院,四川成都610068

出　　处：《乐山师范学院学报》2015年第4期13-17,54,共6页Journal of Leshan Normal University

基　　金：国家自然科学基金"相变动力学理论";项目批准号:11271271;项目代码:0020105401207

摘　　要：文章研究了一类二阶拟线性椭圆方程的Dirichlet问题.首先利用弱连续算子的锐角原理得到了此类方程的弱解存在性,然后运用极值原理,Hlder模估计及H1+α正则性估计对解的正则性进行了提升,最后通过Lp理论得到了强解的存在性和唯一性.This paper has discussed the Dirichlet Prob lem of a class of 2-order quasi-linear elliptic equations. To begin with,Acute-angle Principle for weakly continuous operator is used to get the existence of weak solutions for these equations. Furthermore,the regularity of the solutions has been promoted through a series of theorem on regularity estimation. In conclusion,Lp-estimation theory has guaranteed the existence and uniqueness of the strong solution.

关 键 词：弱解 强解 弱连续算子 正则性估计 

分 类 号：O177.91[理学—数学]