Potential theoretic approach to Schauder estimates for the fractional Laplacian
Potential theoretic approach to Schauder estimates for the fractional Laplacian
复制标题
DOI：
10.1090/proc/13227
复制
发表时间：
2016-02
期刊：
影响因子：
--
通讯作者：
Claudia Bucur;A. Karakhanyan
中科院分区：
文献类型：
--
作者：
Claudia Bucur;A. Karakhanyan
基于Poisson表示公式和并矢球近似论证，给出了方程$（-\Delta）^su（x）=f（x），\，0 <s<1$，其中f$具有连续模$\omega_f$的Schauder估计的初等证明方法.我们给出了u在球B_r（x）\subset \mathbb{R}^n$中关于$\omega_f$的显式连续模。
We present an elementary approach for the proof of Schauder estimates for the equation $(-\Delta)^s u(x)=f(x), \,0<s<1$, with $f$ having a modulus of continuity $\omega_f$, based on the Poisson representation formula and dyadic ball approximation argument. We give the explicit modulus of continuity of $u$ in balls $B_r(x)\subset \mathbb{R}^n$ in terms of $\omega_f$.