Model oblique derivative problem for the heat equation in the Zygmund space H1

The third boundary value problem and the oblique derivative problem for the heat equation are considered in model formulations. A difference compatibility condition is introduced for the initial and boundary functions. Under suitable assumptions made about the problem data, the solutions are shown to belong to the parabolic Zygmund space H1, which is the analogue of the parabolic Hölder space for an integer smoothness exponent.