Nonstationary Venttsel problems with discontinuous data

The paper deals with Venttsel boundary problems for second-order linear and quasilinear parabolic operators with discontinuous principal coefficients. These are supposed to be functions of vanishing mean oscillation with respect to the space variables, while only measurability is required in the time-variable. We derive a priori estimates in composite Sobolev spaces for the strong solutions, and develop maximal regularity and strong solvability theory for such problems. © 2023 The Author(s)