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arXiv · 2005.02584

Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders

Minhyun Kim·Ki-Ahm Lee
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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 $σ\in (0,2)$, the operators under consideration have variable orders of differentiability. Since the order is not characterized by a single number, we consider a function $φ$ describing the variable orders of differentiability, which is allowed to oscillate between two functions $r^{σ_1}$ and $r^{σ_2}$ for some $0 < σ_1 \leq σ_2 < 2$. By introducing the generalized Hölder spaces, we provide $C^{φψ}$ estimates that generalizes the standard Evans--Krylov and Schauder type $C^{σ+α}$ estimates.

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Minhyun Kim, Ki-Ahm Lee. 2020-05-06. Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders. https://doi.org/10.1016/j.jde.2020.08.049

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