Stability of solutions of varying degenerate elliptic equations

Let 1 < p(0) < infinity, s > p(0) and P-i --> p(0). For fixed psi, theta is an element of W-1,W- s(Omega) consider the solution u(i) to the obstacle problem associated with a second order quasilinear degenerate elliptic equation del . A(pi) (x, del u) = 0 with obstacle psi and boundary values theta. Here \A(pi)(x, xi)\ approximate to \xi\(pi) and the functions A(pi) have uniformly bounded structure constants. If for a.e. x is an element of Omega, A(pi) (x, xi) --> A(p0) (x, xi) uniformly on compact subsets of R-n, then it is shown that u(i) --> u(0) in W-1,W- t(Omega) where u(0) is the corresponding solution to del.A(p0) (x, del u) = 0 and t > p(0) depends on n, s, p(0), the structure constants, and the regularity of Omega.