L(1)-contraction and uniqueness for quasilinear elliptic-parabolic equations

We prove the L(I)-contraction principle and uniqueness of solutions for quasilinear elliptic-parabolic equations of the form (o) over cap(t)$[b(u)] - div[a(del u, b(u))] + f(b(u)) = 0 in (0, T) x Omega, where b is monotone nondecreasing and continuous. We assume only that rr is a weak solution of finite-energy. In particular, we do not suppose that the distributional derivative (o) over cap(t)$[b(u)] is a bounded Borer measure or a locally integrable function. (C) 1996 Academic Press, Inc.