... equation. Then, we prove the existence and uniqueness of solutions to the nonhomogeneous A-harmonic equation and the obstacle problem.Keywords: the obstacle problem, the nonhomogeneous A-harmonic ... in the next section. We give the definition of solutions to the nonhomoge-neousA-harmonic equation and the obstacle problem. In the mean time, we s howsome properties of their solutions. Then, ... =(∂1, , ∂n)isthegradientof. The Sobolev space H1,p(Ω) is defined to be the completion of the set { Î C∞(Ω): ||||1,p<∞} with respect to the norm || ·||1,p.Inotherwords,u Î H1,p(Ω)ifandonlyifu...