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NUMBER  
AUTHOR Lee, Ki-Ahm
TITLE Generalized Evans-Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders
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JOURNAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2021
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. (C) 2020 Elsevier Inc. All rights reserved.
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