Weighted variable Lorentz regularity for degenerate elliptic equations in Reifenberg domains. (2nd March 2021)

• Record Type: Journal Article
• Authors: Zhang, Junqiang; Yang, Dachun; Yang, Sibei
• Other Names: Alaoui Mohammed Kbiri guestEditor.; Messaoudi Salim guestEditor.; Hästö Peter guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 14(2022)
• Page Start: 8487
• Page End: 8502
• Publication Date: 2021-03-02
• Subjects: BMO -- degenerate elliptic equation -- Muckenhoupt weight -- Reifenberg flat domain -- variable Lorentz space; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7264
• Languages: English
• ISSNs: 0170-4214

Abstract

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.