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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
- Advisor
- 변순식
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2015-08
- Publisher
- 서울대학교 대학원
- Keywords
- Regularity theory ; Homogenization ; Elliptic system ; BMO space ; Reifenberg 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
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