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Global regularity for quasilinear elliptic equations with Morrey data
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 변순식 | - |
dc.contributor.author | 신필수 | - |
dc.date.accessioned | 2017-07-14T00:42:17Z | - |
dc.date.available | 2017-07-14T00:42:17Z | - |
dc.date.issued | 2016-02 | - |
dc.identifier.other | 000000133110 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121308 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 변순식. | - |
dc.description.abstract | In this thesis, we deal with general quasilinear $m$-Laplacian type operators in divergence form. The nonlinear terms are given by Carath\'eodory functions which are controlled within data belonging to suitable Morrey spaces.
We first prove global boundedness and H\"older continuity up to the boundary for the weak solutions of such equations, generalizing this way the classical $L^p$-result of Ladyzhenskaya and Ural'tseva to the settings of the Morrey spaces. The boundary of the underlying domain is supposed to satisfy a capacity density condition. We also derive global gradient estimates in Morrey spaces for the weak solutions to quasilinear equations having $(\delta,R)$-vanishing nonlinearity. In this case, we assume the boundary of the domain considered is Reifenberg flat which includes boundaries with rough fractal structure. | - |
dc.description.tableofcontents | Chapter 1 Introduction 1
Chapter 2 Auxiliary Results 7 2.1 Notations 7 2.2 Basic tools 10 2.3 Boundary Sobolev inequality 13 Chapter 3 Boundedness and H\"older Continuity 16 3.1 Hypotheses and Main Results 16 3.2 Higher integrability of the gradient 18 3.3 Global Essential Boundedness 29 3.3.1 Proof of Theorem 3.1.1 29 3.3.2 Sharpness of the Hypotheses 36 3.4 Global H\"older Continuity 38 3.4.1 Proof of Theorem 3.1.3 51 3.4.2 H\"older continuity under natural structure conditions 55 Chapter 4 Morrey regularity 57 4.1 Hypotheses and Main Results 57 4.2 Nonlinear elliptic equations 60 4.3 $(\delta,R)$-vanishing properties of superposition operators 61 4.4 Proof of the main results 62 Abstract (in Korean) 74 | - |
dc.format | application/pdf | - |
dc.format.extent | 3100661 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Quasilinear elliptic equation | - |
dc.subject | Global H \"older continuity | - |
dc.subject | Global gradient estimates | - |
dc.subject | Morrey spaces | - |
dc.subject | Irregular domain | - |
dc.subject.ddc | 510 | - |
dc.title | Global regularity for quasilinear elliptic equations with Morrey data | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 74 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2016-02 | - |
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