Solvability of a Model Oblique Derivative Problem for the Heat Equation in the Zygmund Space H1

Abstract

We consider the oblique derivative problem for the heat equation in a model statement. We introduce a difference matching condition for the initial and boundary functions, under which we establish conditions on the data of the problem sufficient for the solution to belong to the parabolic Zygmund space H₁, which is an analog of the parabolic Hölder space for the case of an integer smoothness exponent. We present an example showing that if the above-mentioned matching condition is not satisfied, then the solution may fail to belong to the space H₁.