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Tangential limits of harmonic functions for subordinate Brownian motions : 종속 브라운 운동에 대한 조화함수의 접선극한

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Authors

강재훈

김판기
Major
자연과학대학 수리과학부
Issue Date
2015-02
Publisher
서울대학교 대학원
Keywords
subordinate Brownian motionGreen functionPoisson kernelnon-local operatorharmonic function(non-)tangential limitsFatou theorem
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 2. 김판기.
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 $\beta$.
Language
English
URI
https://hdl.handle.net/10371/121287
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)

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