Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium
Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium
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DOI：
10.1016/j.jfa.2011.11.023
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发表时间：
2011-03
期刊：
影响因子：
--
通讯作者：
Jun Geng;Zhongwei Shen;Liang Song
中科院分区：
文献类型：
--
作者：
Jun Geng;Zhongwei Shen;Liang Song
令 {Lε} 为具有快速振荡周期系数的线弹性椭圆系统族。我们在狄利克雷问题的解中得到统一的W1，估计Rn中的Lipschitz域Ω中的||1p−12|<12n+δ和C,δ>0是独立于ε>0的常数。 n=2 或 3 时范围很窄。
Let {Lε} be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform W1,pestimate ‖∇uε‖p⩽C‖f‖pin a Lipschitz domain Ω in Rnfor solutions to the Dirichlet problem: Lε(uε)=div(f) in Ω and uε=0 on ∂Ω, where |1p−12|<12n+δ and C, δ>0 are constants independent of ε>0. The ranges are sharp for n=2 or 3.