Abstract
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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 433–447, March, 1997.
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Maslov, V.P., Samborskii, S.N. Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations. Ukr Math J 49, 477–493 (1997). https://doi.org/10.1007/BF02487244
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DOI: https://doi.org/10.1007/BF02487244