Maslov V. P.
Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 433–447
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.
Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 737–744
Ukr. Mat. Zh. - 1987. - 39, № 4. - pp. 464–472