  In this paper we consider scalar parabolic equations in a general non-smooth
setting with emphasis on mixed interface and boundary conditions. In
particular, we allow for dynamics and diffusion on a Lipschitz interface and on
the boundary, where diffusion coefficients are only assumed to be bounded,
measurable and positive semidefinite. In the bulk, we additionally take into
account diffusion coefficients which may degenerate towards a Lipschitz
surface. For this problem class, we introduce a unified functional analytic
framework based on sesquilinear forms and show maximal regularity for the
corresponding abstract Cauchy problem.
