Global regularity estimates for a class of quasilinear elliptic equations in the whole space. (May 2020) - Yao, Fengping; Zhang, Chao; Zhou, Shulin
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.