Weighted variable Lorentz regularity for degenerate elliptic equations in Reifenberg domains. (2nd March 2021) - Zhang, Junqiang; Yang, Dachun; Yang, Sibei
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.