Let w be a Muckenhoupt A 2 (ℝ n ) weight and Ω a bounded Reifenberg flat domain in ℝ n . Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition. In this article, the authors investigate the weighted W 1, p (·) (Ω, w )-regularity of the weak solutions of second order degenerate elliptic equations in divergence form with Dirichlet boundary condition, under the assumption that the degenerate coefficients belong to weighted BMO spaces with small norms.

中文翻译：

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Reifenberg 域中退化椭圆方程的加权 W1, p (·)-正则性

令 w 为 Muckenhoupt A 2 (ℝ n ) 权重，Ω 为 ℝ n 中的有界 Reifenberg 平面域。假设 p (·):Ω → (1, ∞) 是满足 log-Hölder 连续条件的变量指数。在本文中，作者在假设退化系数属于具有小范数的加权 BMO 空间。