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Elliptic and parabolic equations with measurable nonlinearities in nonsmooth domains : 매끄럽지 않은 영역에서 정의되고 측정가능한 비선형 계수 함수를 가지는 타원형 및 포물형 편미분 방정식
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- Authors
- Advisor
- 변순식
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2015-08
- Publisher
- 서울대학교 대학원
- Description
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 변순식.
- Abstract
- We study elliptic and parabolic equations with measurable nonlinearities in nonsmooth domains. We establish an optimal global $W^{1,p}$ estimate under the condition that the associated nonlinearity is allowed to be merely measurable in one variable but has a sufficiently small BMO semi-norm in the other variables, while the underlying domain is sufficiently flat in the Reifenberg sense that the boundary of the domain is locally trapped between two narrow strips.
- Language
- English
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