非线性退化椭圆型方程弱解的存在唯一性  

EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

作　　者：陈方敏 严畅 柴晓娟[1] CHEN Fang-min;YAN Chang;CHAI Xiao-juan(School of Mathematical Science,A nhrui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《数学杂志》2021年第5期423-434,共12页Journal of Mathematics

基　　金：国家自然科学基金资助(11701002)。

摘　　要：本文研究了带有退化强制项的非线性椭圆型方程在分布意义下的弱解.利用适当的紧性定理和光滑逼近,在建立逼近方程解的一致正则性和逼近解序列收敛性的基础上,获得了原方程分布意义下弱解的存在性以及逼近解唯一性的结果.In this paper,we consider weak solutions in the distributional sense for nonlinear elliptic equations with degenerate coercivity.By proper compactness theorem and smooth approximation,on the basis of establishing the uniform regularity of solutions of the approximate equations and the convergence of the sequence of approximate solutions,we derive the existence of the weak solution in the distributional sense and the uniqueness of the approximate solution.

关 键 词：退化椭圆方程 分布弱解 逼近解 存在性 唯一性 

分 类 号：O175.25[理学—数学]