论文标题
广义埃文斯 - 非局部完全非线性方程的Krylov和Schauder类型估计值，具有可变订单的粗糙内核
Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders
论文作者
论文摘要
我们建立了具有可变阶的粗糙内核的非本地完全非线性椭圆方程的广义Evans-Krylov和Schauder类型的估计。与具有不同性可与性的固定顺序$σ\ in（0,2）$的固定订单相比，所考虑的运营商具有可变订单的可不同订单。由于该订单未以单个数字为特征，因此我们考虑一个函数$φ$描述可变性的可变顺序，该函数可以在两个函数之间振荡$ r^{σ_1} $和$ r^{σ_2} $，对于一些$ 0 <σ_1<σ_1\ sent = f leqolqσ_2_2<2 $。通过引入广义的Hölder空间，我们提供了$ c^{φψ} $估计，该估计概括了标准的Evans-Krylov和Schauder类型$ C^{σ+α} $估计。
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.
