Global regularity estimates for a class of quasilinear elliptic equations in the whole space

Abstract

In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f∈BMO(Rn)⇒∇u∈BMO(Rn)for the weak solutions of a class of quasilinear elliptic equations diva∇u∇u=divfinRn,where B(t)=∫0tτa(τ)dτ for t≥0. Meanwhile, we use the iteration-covering procedure to prove that Bf∈Lq(Rn)⇒B∇u∈Lq(Rn)for anyq>1for the weak solutions of diva∇u∇u=divaffinRn.Moreover, we remark that a(t)=tp−2(p-Laplace equation)anda(t)=tp−2log(1+t)satisfy the given conditions in this work.