Global regularity estimates for a class of quasilinear elliptic equations in the whole space. (May 2020)

• Record Type: Journal Article
• Authors: Yao, Fengping; Zhang, Chao; Zhou, Shulin
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 35B45 -- 35J60; BMO estimates -- Lq -- Gradient -- Regularity -- Divergence -- Elliptic -- Quasilinear -- p-Laplace; 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.2018.07.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f ∈ B M O ( R n ) ⇒ ∇ u ∈ B M O ( R n ) for the weak solutions of a class of quasilinear elliptic equations div a ∇ u ∇ u = div f in R n, where B ( t ) = ∫ 0 t τ a ( τ ) d τ for t ≥ 0 . Meanwhile, we use the iteration-covering procedure to prove that B f ∈ L q ( R n ) ⇒ B ∇ u ∈ L q ( R n ) for any q > 1 for the weak solutions of div a ∇ u ∇ u = div a f f in R n . Moreover, we remark that a ( t ) = t p − 2 ( p -Laplace equation) and a ( t ) = t p − 2 log ( 1 + t ) satisfy the given conditions in this work.