Weighted variable Lorentz regularity for degenerate elliptic equations in Reifenberg domains

Abstract

Let w be a Muckenhoupt A 2 (R n ) weight and Ω a Reifenberg flat domain in R n . Assume that q ∈ (0, ∞] and p(•) : Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition. In this article, the authors investigate the weighted variable Lorentz L p(•), q (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.