Weighted gradient estimates for higher order elliptic systems with non-smooth coefficients. (May 2020)

• Record Type: Journal Article
• Authors: Bui, The Anh; Bui, The Quan
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 35J48 -- 35B65; Higher-order elliptic systems -- Lipschitz domain -- Weighted Lorentz spaces -- Lorentz–Morrey spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.10.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove the regularity estimates on the weighted Lorentz spaces for the higher-order elliptic system of equations with non-smooth coefficients on a Lipschitz domain. As a by product, we obtain the regularity estimate on the Lorentz–Morrey spaces. Our results extend previous results to the larger class of Muckenhoupt weights.