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W1,p estimates in homogenization of elliptic systems with measurable coefficients in nonsmooth domains
부드럽지 않은 영역에서 측정가능한 계수를 가지는 타원형 연립 방정식의 균질화 문제에 대한 W1,p 가늠

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Authors
장윤수
Advisor
변순식
Major
자연과학대학 수리과학부
Issue Date
2015-08
Publisher
서울대학교 대학원
Keywords
Regularity theoryHomogenizationElliptic systemBMO spaceReifenberg domain
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 변순식.
Abstract
In this study, we establish uniform $W^{1,p}$ estimates for weak solutions in homogenization of elliptic systems in divergence-form with measurable coefficients in nonsmooth domains. We consider first an interior regularity and then we study boundary value problems, a Dirichlet problem and a conormal derivative problem. Our main purpose is to find an answer for minimal requirements on the coefficients and the boundary condition of the domains to ensure that Calder\'{o}n-Zygmund theory holds in a homogenization problem.
Language
English
URI
https://hdl.handle.net/10371/121294
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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