Regularity for nonlocal operators with kernels of functional order
함수적 차수의 커널을 갖는 비국소 작용소의 정칙성

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dc.description학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 김판기.-
dc.description.abstractIn 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.
dc.description.tableofcontentsChapter 1. Introduction 1

Chapter 2. Holder estimates for fully nonlinear equations 5
2.1. Setting and main results 6
2.2. Viscosity solution and elliptic operator 10
2.3. The proof of Theorem 2.1.1 11
2.4. Example: Isotropic unimodal Levy process 22

Chapter 3. Schauder estimates in generalized Holder spaces 25
3.1. Setting and main results 26
3.2. Generalized Holder spaces 30
3.3. The translation invariant case 39
3.3.1. Semigroup of subordinate Brownian motion 40
3.3.2. Proof of Theorem 3.1.1 42
3.4. Proof of Theorem 3.1.2 48
3.5. Continuity of L 62

Bibliography 65

국문초록 70
dc.format.extent2052718 bytes-
dc.publisher서울대학교 대학원-
dc.subjectNonlocal operator-
dc.subjectHolder continuity-
dc.subjectSchauder estimate-
dc.subjectLevy process-
dc.titleRegularity for nonlocal operators with kernels of functional order-
dc.title.alternative함수적 차수의 커널을 갖는 비국소 작용소의 정칙성-
dc.contributor.AlternativeAuthorJongchun Bae-
dc.citation.pagesii, 69-
dc.contributor.affiliation자연과학대학 수리과학부-
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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