On sufficient conditions for generalized solutions of some mixed parabolic problems to be classical

Abstract

Considering the mixed problem for the second order linear parabolic equation with the Dirichlet boundary condition, we obtain new sufficient conditions under which the generalized solution to the problem is classical. These conditions are formulated in terms of the belonging of the right-hand sides of the problem to certain $2b$-anisotropic H\"{o}rmander spaces. The classical solutions can be discontinuous on the junction of the lateral area and base of the cylinder in which the problem is considered.