Weighted W1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains

Abstract

Let w be a Muckenhoupt A2(ℝn) weight and Ω a bounded Reifenberg flat domain in ℝn. Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition. In this article, the authors investigate the weighted W1, 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.

Keywords

• reifenberg flat domain
• degenerate elliptic equation
• muckenhoupt weight
• variable lebesgue space
• bmo
• primary 35j70
• secondary 35b65
• 46e35
• 42b35
• 42b37