一类非线性椭圆问题解的正则性  

Regularity for some nonlinear elliptic problems

作　　者：黄苗苗 赵雪漪 冯贺平[3] HUANG Miaomiao;ZHAO Xueyi;FENG Heping(College of Mathematics and Computer Science,Hanjiang Normal University,Shiyan 442000,China;Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062,China;Intelligent Engineering Department,Hebei Software Institute,Baoding 071002,China)

机构地区：[1]汉江师范学院数学与计算机科学学院,湖北十堰442000 [2]湖北大学应用数学湖北省重点实验室,湖北武汉430062 [3]河北软件职业技术学院智能工程系,河北保定071002

出　　处：《河北大学学报（自然科学版）》2023年第3期225-229,共5页Journal of Hebei University(Natural Science Edition)

基　　金：应用数学湖北省重点实验室(湖北大学)开放基金资助项目(HBAM202003);湖北省高等学校优秀中青年科技创新团队项目(T2022035)。

摘　　要：研究椭圆型偏微分方程的源函数是关于自变量、自变量的未知函数及未知函数的偏导数的函数时,非线性椭圆方程的边值问题.利用推广的Stampacchia引理以及Sobolev空间的分析技巧,得到椭圆型方程的边值问题在强制性和控制增长条件下解的正则性.When the source function of elliptic partial differential equation is a function of independent variable,unknown function of independent variable and partial derivative of unknown function,the boundary value problem of nonlinear elliptic equation is studied.By using the generalized Stampacchia lemma and the analysis technique of Sobolev space,the regularity of the solution of the boundary value problem of elliptic equation under some coercivity and controlled growth assumptions is obtained.

关 键 词：正则性 椭圆型方程 边值问题 Stampacchia引理 

分 类 号：O175.23[理学—数学]