Regularity for fully nonlinear integro-differential operators with kernels of variable orders. (April 2020)

• Record Type: Journal Article
• Authors: Kim, Minhyun; Lee, Ki-Ahm
• Is Part Of: Nonlinear analysis. Volume 193(2020)
• Publication Date: 2020-04
• Subjects: 35J60 -- 47G20 -- 35B65; Nonlinear elliptic equations -- Integro-differential operators -- Smoothness and regularity of solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.07.009
• Languages: English
• ISSNs: 0362-546X

Abstract

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 φ = ∫ R n 1 − cos y 1 | y | n φ ( | y | ) d y − 1 instead of 2 − σ, where φ satisfies a weak scaling condition. We obtain the uniform Harnack inequality and Hölder estimates of viscosity solutions to the nonlinear integro-differential equations.