The Space $H_p$ of Solutions of Degenerate Parabolic Equations

In a cylinder $Q$ whose base is bounded by a Lyapunov surface, a second-order parabolic equation degenerate in the tangent directions to the boundary of the base is considered. For solutions of this equation, a class $H_p$ is introduced by analogy with the elliptic case. A criterion for a function to belong to this class is found. Conditions for the unique solvability of the problem with boundary and initial conditions understood in the sense of $L_p$ are given.