A-调和方程组很弱解的正则性  

Regularity of Very Weak Solutions to A-harmonic Systems

作　　者：赵青 ZHAO Qing(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2018年第1期1-11,共11页Journal of Minnan Normal University：Natural Science

基　　金：国家自然科学基金(11571159);福建省中青年教师教育科研项目(JAT170339);福建省自然科学基金(2016J01026)

摘　　要：利用Hodge分解定理,借助Hlder不等式,Poincáre不等式及Young不等式等技巧,提高了一类非齐次A-调和方程组很弱解偏微商的可积性.进一步地,基于A-调和逼近方法,得到了很弱解的最优部分正则性结果.Applying Hodge decomposition theorem,the integrability of the derivative of very weak solutions is improved to some nonhomogeneous A-harmonic systems with the aid of Holder’s inequality,Poincáre’s inequality and Young’s inequality etc.Further,these solutions are proved to be optimal Holder continuity based on A-harmonic approximation technique.

关 键 词：非齐次A-调和方程组 很弱解 最优部分正则性 HODGE分解 A-调和逼近方法 

分 类 号：O175.23[理学—数学]