Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations
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.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 3, pp 477-493.
Citation Example: Maslov V. P., Samborsky S. N. Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations // Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 433–447.