Global Calderón-Zygmund estimates for a class of nonlinear elliptic equations with Neumann data

In this paper we obtain the following global Calderón-Zygmund estimatesB(|f|)∈Lq(Ω)⇒B(|∇u|)∈Lq(Ω)for anyq≥1 in a convex domain Ω of the weak solution for a class of quasilinear elliptic equations with the Neumann datadiv(a(|∇u|)∇u)=div(a(|f|)f)inΩ,a(|∇u|)∇u⋅ν=a(|f|)f⋅νon∂Ω, where B(t)=∫0tτa(τ)dτ for t≥0. Moreover, we remark thatB(t)=tplog⁡(1+t) satisfies the given conditions in this work.