Boundary estimates for solutions to operators of p-Laplace type with lower order terms

In this paper we study the boundary behavior of solutions to equations of the form∇⋅A(x,∇u)+B(x,∇u)=0,∇⋅A(x,∇u)+B(x,∇u)=0, in a domain Ω⊂RnΩ⊂Rn, assuming that Ω is a δ-Reifenberg flat domain for δ sufficiently small. The function A is assumed to be of p-Laplace character. Concerning B  , we assume that |∇ηB(x,η)|⩽c|η|p−2|∇ηB(x,η)|⩽c|η|p−2, |B(x,η)|⩽c|η|p−1|B(x,η)|⩽c|η|p−1, for some constant c  , and that B(x,η)=|η|p−1B(x,η/|η|)B(x,η)=|η|p−1B(x,η/|η|), whenever x∈Rnx∈Rn, η∈Rn∖{0}η∈Rn∖{0}. In particular, we generalize the results proved in J. Lewis et al. (2008) [12] concerning the equation ∇⋅A(x,∇u)=0∇⋅A(x,∇u)=0, to equations including lower order terms.