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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
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 변순식 | - |
| dc.contributor.author | 김유찬 | - |
| dc.date.accessioned | 2017-07-14T00:41:41Z | - |
| dc.date.available | 2017-07-14T00:41:41Z | - |
| dc.date.issued | 2015-08 | - |
| dc.identifier.other | 000000056890 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/121296 | - |
| dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 변순식. | - |
| dc.description.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. | - |
| dc.description.tableofcontents | Abstract i
1 Introduction 1 2 Elliptic equations 5 2.1 Definitions and main result 5 2.2 Preliminaries 8 2.3 Lipschitz regularity for limiting equations 13 2.3.1 Interior Lipschitz regularity for limiting equations 14 2.3.2 Boundary Lipschitz regularity for limiting equations 17 2.4 Comparison estimates 22 2.4.1 Interior comparison estimates 22 2.4.2 Boundary comparison estimates 25 2.5 Global estimates in Reifenberg flat domains 32 3 Parabolic equations 44 3.1 Definitions and main result 44 3.2 Preliminaries 48 3.3 Lipschitz regularity for limiting equations 53 3.3.1 Interior Lipschitz regularity for limiting equations 54 3.3.2 Boundary Lipschitz regularity for limiting equations 65 3.4 Comparison estimates 80 3.4.1 Interior comparison estimates 81 3.4.2 Boundary comparison estimates 83 3.5 Global estimates in Reifenberg flat domains 92 Abstract (in Korean) 108 | - |
| dc.format | application/pdf | - |
| dc.format.extent | 3190712 bytes | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject | Calderon-Zygmund estimate | - |
| dc.subject | nonlinear elliptic equation | - |
| dc.subject.ddc | 510 | - |
| dc.title | Elliptic and parabolic equations with measurable nonlinearities in nonsmooth domains | - |
| dc.title.alternative | 매끄럽지 않은 영역에서 정의되고 측정가능한 비선형 계수 함수를 가지는 타원형 및 포물형 편미분 방정식 | - |
| dc.type | Thesis | - |
| dc.contributor.AlternativeAuthor | Youchan Kim | - |
| dc.description.degree | Doctor | - |
| dc.citation.pages | iii,108 | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2015-08 | - |
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