Abstract The paper concerns regularities of solutions of elliptic equations in non-divergence form with directional homogenization. The main interest is to investigate the differences of regularities of datums that are needed and of solutions that are obtained between directions with homogenization and without homogenization. We establish uniform interior L p ( 1 p ≤ ∞ ) estimates for D 2 u e and uniform interior C γ ( 0 ≤ γ 1 ) estimates for D D x ′ u e , where x ′ are the non-homogenization directions. Our results are optimal.

中文翻译：

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非发散形式椭圆方程的方向齐化

摘要 本文研究了具有方向均匀化的非发散形式椭圆方程解的规律性。主要兴趣是研究所需基准的规律性和均匀化和非均匀化方向之间获得的解的差异。我们为 D 2 ue 建立统一的内部 L p ( 1 p ≤ ∞ ) 估计和为 DD x ' ue 建立统一的内部 C γ ( 0 ≤ γ 1 ) 估计，其中 x ' 是非均质化方向。我们的结果是最优的。