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Regularity for nonlocal operators with kernels of functional order : 함수적 차수의 커널을 갖는 비국소 작용소의 정칙성
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- Authors
- Advisor
- 김판기
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2016-02
- Publisher
- 서울대학교 대학원
- Keywords
- Nonlocal operator ; Holder continuity ; Schauder estimate ; Levy process
- Description
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 김판기.
- Abstract
- In this thesis, we investigate the regularity results for nonlocal operators with kernels of functional order. We consider a nonlocal operator for a given jumping kernel comparable to a special function near zero. Assuming the function has a weak scaling condition one can generalize the fractional Laplace operator. Firstly, we obtain the Holder continuity of solutions to fully nonlinear nonlocal equations with respect to a certain class of linear nonlocal operators in analytic method. Secondly, we prove the Schauder estimates for
nonlocal equation by introducing the generalized Holder spaces.
- Language
- English
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