一类非齐次A-调和方程很弱解的全局正则性  

Global regularity for very weak solutions to non-homogeneous A-harmonic equation

作　　者：徐秀娟 闫硕 朱叶青 XU Xiu-juan;YAN Shuo;ZHU Ye-qing(College of Science,North China University of Science and Technology,Tangshan 063210,Hebei,China)

机构地区：[1]华北理工大学理学院,河北唐山063210

出　　处：《山东大学学报（理学版）》2020年第2期48-56,67,共10页Journal of Shandong University(Natural Science)

摘　　要：研究形如div A(x,▽u)=f(x)的非齐次A-调和方程的边值问题,在控制增长条件、强制性条件以及非齐次项的适当可积性假设条件下,利用Hodge分解定理和Sobolev空间分析方法,得到了很弱解的全局正则性,推广了已知的结果。This paper deals with boundary value problem for non-homogeneous A-harmonic equation div(A(x,▽u))=f(x).A global regularity result is derived for very weak solutions under some controllable and coercivity conditions and some proper integrable assumptions on the nonlinear term,by using the Hodge decomposition theorem and the methods in Sobolev spaces.The results generalize the corresponding results in related literatures.

关 键 词：非齐次A-调和方程 HODGE分解 全局正则性 

分 类 号：O175.25[理学—数学]