This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a C1,1 domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.

中文翻译：

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加权变量 Lebesgue 空间上非散度椭圆方程的全局正则估计

本文旨在证明具有 BMO 系数的非散度形式的二阶椭圆方程解的全局正则性估计C1,1加权变量指数 Lebesgue 空间上的域。我们的方法基于非发散椭圆方程的解的表示和谐波分析中稀疏算子的支配技术。