Publications
Detailed Information
Tangential limits of harmonic functions for subordinate Brownian motions : 종속 브라운 운동에 대한 조화함수의 접선극한
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 김판기 | - |
dc.contributor.author | 강재훈 | - |
dc.date.accessioned | 2017-07-14T00:41:16Z | - |
dc.date.available | 2017-07-14T00:41:16Z | - |
dc.date.issued | 2015-02 | - |
dc.identifier.other | 000000024985 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121287 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 2. 김판기. | - |
dc.description.abstract | In this thesis, we study the integral kernel and boundary behavior of harmonic functions for certain non-local operators. First, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided Poisson kernel estimates for pure-jump subordinate Brownian motions including geometric stable processes. The infinitesimal generators of pure-jump subordinate Brownian motions are non-local operators. Second, we show the existence of tangential limits of regular harmonic functions with respect to such non-local operators in $C^{1,1}$ open sets when the exterior functions are local $L_p$-H\"older continuous functions of order $\beta$. | - |
dc.description.tableofcontents | Abstract i
1 Introduction 1 2 Preliminaries 5 2.1 Subordinate Brownian motion 5 2.2 Assumptions on $\phi$ 9 3 Poisson kernel estimates 13 3.1 Poisson kernel estimates for subordinate Brownian motion 13 3.2 Proof of Poisson kernel estimates 15 4 Tangential limits for harmonic functions 37 4.1 Main theorem 37 4.2 Analysis on Lipschitz open set 40 4.3 Proof of Theorem 4.1.3 49 Abstract (in Korean) 58 | - |
dc.format | application/pdf | - |
dc.format.extent | 2019720 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | subordinate Brownian motion | - |
dc.subject | Green function | - |
dc.subject | Poisson kernel | - |
dc.subject | non-local operator | - |
dc.subject | harmonic function | - |
dc.subject | (non-)tangential limits | - |
dc.subject | Fatou theorem | - |
dc.subject.ddc | 510 | - |
dc.title | Tangential limits of harmonic functions for subordinate Brownian motions | - |
dc.title.alternative | 종속 브라운 운동에 대한 조화함수의 접선극한 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Jaehoon Kang | - |
dc.description.degree | Doctor | - |
dc.citation.pages | ii, 58 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2015-02 | - |
- Appears in Collections:
- Files in This Item:
Item View & Download Count
Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.