Korn's Inequality and Divergence Equations on Generalize Orlicz Spaces  

广义的Orlicz空间上的Korn不等式与散度方程

作　　者：WU Rui-min WANG Song-bai 

机构地区：[1]School of Longqiao College of Lanzhou University of Finance and Economics,Lanzhou 730101,China [2]School of College of Mathematics and Statistics,Chongqing Three Gorges University,Chongqing 4-04-130,China

出　　处：《Chinese Quarterly Journal of Mathematics》2020年第4期344-353,共10页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.11726622);Scientific Research Fund of Young Teachers in Longqiao College (Grant No. LQKJ2020-01)。

摘　　要：Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we generalize Korn's inequality to the setting of generalized Orlicz spaces, i.e., ‖■f‖Lφ(·)(Ω)■‖Df‖Lφ(·)(Ω). Using the Calderón–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu = f has a solution u ∈(W^1φ(·)(Ω)0)^n such that ‖■f‖Lφ(·)(Ω)■‖f‖Lφ(Ω).

关 键 词：Generalized Orlicz spaces Korn's inequality EXTRAPOLATION 

分 类 号：O174.2[理学—数学]