Abstract:
Considered a second-order parabolic equation in the cylinder $Q$ whose base is bounded by the Lyapunov surface. It is assumed that this equation is degenerated with respect to tangential directions. The class $H_p$ is introduced for solutions of the equation analogously to elliptic case. The criterion of belonging of functions to this class is established. The conditions of unique solvability of the problem with boundary and initial conditions, understood in the sense of $L_p$ , are given.
Keywords:degenerate parabolic equations, second order, boundary values in the sense of.
