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Regularity theory for elliptic and parabolic equations in nondivergence form

DC Field Value Language
dc.contributor.advisor변순식-
dc.contributor.author이미경-
dc.date.accessioned2017-07-14T00:42:05Z-
dc.date.available2017-07-14T00:42:05Z-
dc.date.issued2016-02-
dc.identifier.other000000132440-
dc.identifier.urihttps://hdl.handle.net/10371/121304-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 변순식.-
dc.description.abstractWe investigate optimal regularity theory for nondivergence elliptic and parabolic equations with discontinuous coefficients in bounded domains.
Global Hessian estimates of the solutions to the Dirichlet problems for such equations are obtained under the small bounded mean oscillation (BMO) condition of the coefficients in the setting of various function spaces such as weighted Lebesgue spaces, variable exponent Lebesgue spaces, weighted Orlicz spaces and weighted variable exponent Lebesgue spaces.		-
dc.description.tableofcontentsChapter 1 Introduction 1

Chapter 2 Regularity theory for nondivergence elliptic equations 8
2.1 Preliminary results 10
2.2 Weighted W 2,p-estimates 23
2.2.1 Preliminaries and main result 23
2.2.2 Interior weighted estimates 28
2.2.3 Boundary weighted estimates 34
2.2.4 Global weighted estimates 42
2.3 W 2,p()-estimates 47
2.3.1 Preliminaries and main result 47
2.3.2 Interior and boundary W 2,p()-estimates 50
2.3.3 Global W 2,p()-estimates 63

Chapter 3 Regularity theory for nondivergence parabolic equations 68
3.1 Preliminary results 70
3.2 Weighted estimates in Orlicz spaces 81
3.2.1 Assumptions and main result 81
3.2.2 Preliminaries 86
3.2.3 Interior and boundary weighted Orlicz estimates 88
3.2.4 Global weighted Orlicz estimates 102
3.3 Weighted estimates in variable exponent spaces 107
3.3.1 Assumptions and main result 107
3.3.2 Preliminaries 111
3.3.3 Interior and boundary weighted W 2,1,p()-estimates 117
3.3.4 Global weighted W 2,1,p()-estimates 132

Bibliography 140

Abstract (in Korean) 147		-
dc.formatapplication/pdf-
dc.format.extent1933142 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectRegularity-
dc.subjectnondivergence elliptic equation-
dc.subjectnondivergence parabolic equation-
dc.subjectstrong solution-
dc.subjectBMO space-
dc.subjectweighted Lebesgue space-
dc.subjectOrlicz space-
dc.subjectvariable exponent Lebesgue space-
dc.subject.ddc510-
dc.titleRegularity theory for elliptic and parabolic equations in nondivergence form-
dc.typeThesis-
dc.description.degreeDoctor-
dc.citation.pages147-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2016-02-
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