A priori estimate for the second-order derivatives of solutions to the Dirichlet problem for fully nonlinear parabolic equations

The first initial-boundary-value problem for a uniformly parabolic and uniformly nondegenerate operator is considered. An a priori estimate for an admissible solution is established. In view of the generalized Hessian, it is possible to avoid the growth conditions which are usual in the theory of uniformly elliptic and uniformly parabolic operators. Bibliography: 19 titles.