Conditions for solutions of the second boundary-value problem for parabolic equations to be classical

Abstract

Considering the initial-boundary value problem for the second order linear parabolic equation with the general boundary condition of first order, 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 $2$-anisotropic H\"ormander 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.