A-调和方程障碍问题弱解的全局正则性  

Global regularity for weak solutions to obstacle problem of the A-Harmonic equation

作　　者：朱叶青 周艳霞 佟玉霞 ZHU Yeqing;ZHOU Yanxia;TONG Yuxia(College of Science,North China University of Science and Technology,Tangshan 063210,China)

机构地区：[1]华北理工大学理学院,唐山063210

出　　处：《黑龙江大学自然科学学报》2020年第6期675-681,共7页Journal of Natural Science of Heilongjiang University

基　　金：河北省自然科学基金资助项目(A2019209005)。

摘　　要：在R^n(n≥2)中的有界区域Ω的边界■Ω满足可测密度条件下,研究了非齐次A-调和方程-divΑ(x,■u)=-divF(x)对应的障碍问题的弱解。通过建立全局逆H■lder不等式,借助H■lder不等式、Young不等式及Gehring引理等工具,得出该方程障碍问题弱解的全局正则性。Under the condition that the boundary■Ωof the bounded regionΩin R^n(n≥2)satisfies the measurable density,the weak solution of the obstacle problem corresponding to the nonhomogeneous A-Harmonic equation-divΑ(x,■u)=-divF(x)is considered.By establishing the global inverse H■lder inequality and using the tools such as H■lder inequality,Young inequality and Gehring lemma,the global regularity of the weak solution of the obstacle problem is obtained.

关 键 词：A-调和方程 Kψ^θ p-障碍问题 弱解 全局正则性 

分 类 号：O175.25[理学—数学]