带变阶粗糙核的非局部完全非线性方程的广义Evans--Krylov型与Schauder型估计
Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders
AI总结：
该研究针对带变阶粗糙核的非局部完全非线性椭圆方程，引入描述可变可微阶数的函数与广义Hölder空间，建立了推广标准结果的广义Evans--Krylov型与Schauder型$C^{\phi\psi}$估计。
摘要：
我们针对带变阶粗糙核的非局部完全非线性椭圆方程，建立了广义Evans--Krylov型与Schauder型估计。与具有固定可微阶数$\sigma\in(0,2)$的分数阶Laplacian型算子不同，本文研究的算子具有可变的可微阶数。由于阶数无法用单个数值表征，我们引入一个描述可变可微阶数的函数$\phi$，它允许在$0 < \sigma_1 \leq \sigma_2 < 2$对应的两个函数$r^{\sigma_1}$与$r^{\sigma_2}$之间振荡。通过引入广义Hölder空间，我们给出了$C^{\phi\psi}$估计，该估计推广了标准的Evans--Krylov型与Schauder型$C^{\sigma+\alpha}$估计。
英文摘要：
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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