L1-Contraction and Uniqueness for Quasilinear Elliptic–Parabolic Equations

We prove theL1-contraction principle and uniqueness of solutions for quasilinear elliptic–parabolic equations of the form[formula]wherebis monotone nondecreasing and continuous. We assume only thatuis a weak solution of finite energy. In particular, we donotsuppose that the distributional derivative ∂t[b(u)] is a bounded Borel measure or a locally integrable function.