L1-Contraction and Uniqueness for Quasilinear Elliptic–Parabolic Equations

Abstract We prove the L 1 -contraction principle and uniqueness of solutions for quasilinear elliptic–parabolic equations of the form[formula]where b is monotone nondecreasing and continuous. We assume only that u is a weak solution of finite energy. In particular, we do not suppose that the distributional derivative ∂ t [ b ( u )] is a bounded Borel measure or a locally integrable function.