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	Convergence rates and W-1,W-P estimates in homogenization theory of Stokes systems in Lipschitz domains
	Xu, Qiang
	2017
关键词	Homogenization Stokes systems Convergence rates Lipschitz domains W-1,W-p estimates PERIODIC HOMOGENIZATION ELLIPTIC-SYSTEMS DIRICHLET PROBLEM OPERATOR COEFFICIENTS
英文摘要	Concerned with the Stokes systems with rapidly oscillating periodic coefficients, we mainly extend the recent works in [19,20] to those in term of Lipschitz domains. The arguments employed here are quite different from theirs, and the basic idea comes from [37], originally motivated by [23,27,33]. We obtain 24 an almost-sharp O(epsilon ln(r(0)/epsilon)) convergence rate in L-2 space, and a sharp O(epsilon) error estimate in L2d/d-1 space by a little stronger assumption. Under the dimensional condition d = 2, we also establish the optimal O(epsilon) convergence rate on pressure terms in L-2 space. Then utilizing the convergence rates we can derive the W-1,W-P estimates uniformly down to microscopic scale e without any smoothness assumption on the coefficients, where vertical bar 1/p - 1/2 vertical bar < 1/2d + epsilon and epsilon is a positive constant independent of epsilon. Combining the local estimates, based upon VMO coefficients, consequently leads to the uniform W-1,W-P estimates. Here the proofs do not rely on the well known compactness methods. (C) 2017 Elsevier Inc. All rights reserved.; National Natural Science Foundation of China [11471147]; SCI(E); ARTICLE; 1; 398-450; 263
语种	英语
出处	SCI
出版者	JOURNAL OF DIFFERENTIAL EQUATIONS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/472260]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xu, Qiang. Convergence rates and W-1,W-P estimates in homogenization theory of Stokes systems in Lipschitz domains. 2017-01-01.

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