ON THE SMOOTHNESS OF THE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR PARABOLIC AND DEGENERATE ELLIPTIC EQUATIONS

We investigate the question of smoothness for solutions of the first and second boundary problems for a class of degenerate equations (including, in particular, a parabolic equation) in domains with boundaries containing characteristic points. In the case of tangency of higher degree of the boundary with a characteristic plane conditions are given which guarantee that the solution belongs to the space Hp. Bibliography: 9 items.