Generalized Evans-Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable ordersopen access
- Authors
- Kim, Minhyun; Lee Ki-Ahm
- Issue Date
- Jan-2021
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, v.270, pp.883 - 915
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF DIFFERENTIAL EQUATIONS
- Volume
- 270
- Start Page
- 883
- End Page
- 915
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/190341
- DOI
- 10.1016/j.jde.2020.08.049
- ISSN
- 0022-0396
- Abstract
- We establish the generalized Evans-Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to the fractional Laplacian type operators having a fixed order of differentiability sigma is an element of (0, 2), the operators under consideration have variable orders of differentiability. Since the order is not characterized by a single number, we consider a function phi describing the variable orders of differentiability, which is allowed to oscillate between two functions r(sigma 1) and r(sigma 2) for some 0 < sigma(1) <= sigma(2) < 2. By introducing the generalized Holder spaces, we provide C-phi psi estimates that generalizes the standard Evans-Krylov and Schauder type C sigma+alpha estimates.
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