Abstract:
In part I normalized parabolic Bellman equations of the form Fu=0 were studied; in this part ordinary Bellman equations, i.e. equations solved for the derivative with respect to t, are considered. While it was assumed in part I that the un and u have bounded weak derivatives with respect to t, it is merely assumed here that they are of bounded variation with respect to t. As before, the second derivatives with respect to x of the convex (in x) functions un and u are understood in the generalized sense (as measures), while the equations Fun=0 and Fu=0 are considered in a lattice of measures.
Bibliography: 4 titles.
This publication is cited in the following 5 articles:
N. V. Krylov, “On degenerate nonlinear elliptic equations. II”, Math. USSR-Sb., 49:1 (1984), 207–228
P. L. Lions, “Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations part 2 : viscosity solutions and uniqueness”, Communications in Partial Differential Equations, 8:11 (1983), 1229
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Math. USSR-Izv., 20:3 (1983), 459–492
N. V. Krylov, “On controlled diffusion processes with unbounded coefficients”, Math. USSR-Izv., 19:1 (1982), 41–64
N. V. Krylov, “Some new results in the theory of controlled diffusion processes”, Math. USSR-Sb., 37:1 (1980), 133–149