Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations - Maslov, V. P.; Samborsky, S. N. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We introduce solutions of boundary-value problems for the stationary Hamilton-Jacobi and Bellman equations in functional spaces (semimodules) with a special algebraic structure adapted to these problems. In these spaces, we obtain representations of solutions in terms of “basic” ones and prove a theorem on approximation of these solutions in the case where nonsmooth Hamiltonians are approximated by smooth Hamiltonians. This approach is an alternative to the maximum principle.