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Regularity for fully nonlinear integro-differential operators with kernels of variable orders
- Authors
- Kim, Minhyun; Lee, Ki-Ahm
- Issue Date
- Apr-2020
- Publisher
- PERGAMON-ELSEVIER SCIENCE LTD
- Keywords
- Nonlinear elliptic equationsIntegro-differential operatorsSmoothness and regularity of solutions
- Citation
- NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v.193, pp.1 - 27
- Indexed
- SCIE
SCOPUS
- Journal Title
- NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
- Volume
- 193
- Start Page
- 1
- End Page
- 27
- ISSN
- 0362-546X
- Abstract
- We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in Caffarelli and Silvestre (2009). Since the order of differentiability of the kernel is not characterized by a single number, we use the constant,C-phi = (integral(Rn) 1-COS y1/ vertical bar y vertical bar(n)phi (vertical bar y vertical bar) dy)(-1),instead of 2 - sigma, where phi satisfies a weak scaling condition. We obtain the uniform Harnack inequality and Holder estimates of viscosity solutions to the nonlinear integro-differential equations. (C) 2018 Elsevier Ltd. All rights reserved.,
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Related Researcher
- Kim, Minhyun
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)