Boundary regularity for nonlocal operators with kernels of variable ordersopen access
- Authors
- Kim, Minhyun; Kim, Panki; Lee, Jaehun; Lee, Ki-Ahm
- Issue Date
- Jul-2019
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Nonlocal operator; Dirichlet problem; Boundary regularity
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v.277, no.1, pp.279 - 332
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume
- 277
- Number
- 1
- Start Page
- 279
- End Page
- 332
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189460
- DOI
- 10.1016/j.jfa.2018.11.011
- ISSN
- 0022-1236
- Abstract
- We study the boundary regularity of solutions of the Dirichlet problem for the nonlocal operator with a kernel of variable orders. Since the order of differentiability of the kernel is not represented by a single number, we consider the generalized Holder space. We prove that there exists a unique viscosity solution of Lu = f in D, u = 0 in R-n\D, where D is a bounded C-1,C-1 open set, and that the solution u satisfies u is an element of C-V(D) and u/V(d(D)) is an element of C-alpha(D) with the uniform estimates, where V is the renewal function and d(D)(x) = dist(x, partial derivative D).
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