S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Regularity for nonlocal operators with kernels of functional order : 함수적 차수의 커널을 갖는 비국소 작용소의 정칙성
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 김판기.
- 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.