Boundary Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems

for all v∈ ={v∈W 0 (Ω), v≥ψ a.e. in Ω}. Here Ω is a bounded domain in RN (N≥2) with Lipschitz boundary, 2≤ p ≤N . A(x,ξ) :Ω×RN → RN satisfies the following conditions: (i) A is a vector valued function, the mapping x → A(x,ξ) is measurable for all ξ ∈ RN , ξ → A(x,ξ) is continuous for a.e. x ∈Ω; (ii) the homogeneity condition: A(x, tξ)= t|t|p−2A(x,ξ), t ∈ R, t = 0; (iii) the monotone inequality: (A(x,ξ)−A(x,ζ))(ξ − ζ)≥ a|ξ − ζ|p; (iv) |h||ai j|+ |∂Ai(x,h)/∂xj| ≤ τ1|h|p−1; (v) ∑N i, j=1 ai ξiξ j ≥ τ2|h|p−2|ξ|2; (vi) |A(x,ξ)−A(y,ξ)| ≤ b1(1+ |ξ|p−1)|x− y|α0 ; (vii) |A(x,ξ)−A(x,η)| ≤ b2||ξ|p−2ξ −|η|p−2η|; where ai j = ∂A/∂hj , a, b1, b2, τ1, τ2 are positive constants.