一类非齐次椭圆方程组非常弱解的正则性  

Regularity of very weak solutions for a class of inhomogeneous elliptic equations

作　　者：陈淑红 CHEN Shuhong(School of Mathematics and Computer,Wuyi University,Wuyishan 354300,Fujian Province,China)

机构地区：[1]武夷学院数学与计算机学院,福建武夷山354300

出　　处：《浙江大学学报（理学版）》2023年第1期25-29,48,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11571159);武夷学院引进人才科研启动项目(YJ202118)。

摘　　要：研究一类非齐次项是p-Laplace算子的椭圆方程组非常弱解的正则性。结合Hodge分解以及偏微分方程正则性理论的证明技巧,建立了具有p-Laplace型椭圆方程组的非常弱解与经典意义下的弱解之间的关系。In this paper, we study the regularity theory of very weak solutions for a class of elliptic equations which inhomogeneous terms are p-Laplace operators. Combining Hodge decomposition and the regularity theory of partial differential equations, the relation between the very weak solution of p-Laplacian elliptic equations and the weak solution in the classical sense is established.

关 键 词：p-Laplace型 非常弱解 HODGE分解 正则性 

分 类 号：O175.2[理学—数学]