On Aronsson Equation and Deterministic Optimal Control |
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Authors: | Pierpaolo Soravia |
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Institution: | (1) Dipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste 63, 35121 Padova, Italy |
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Abstract: | When Hamiltonians are nonsmooth, we define viscosity solutions of the Aronsson equation and prove that value functions of
the corresponding deterministic optimal control problems are solutions if they are bilateral viscosity solutions of the Hamilton-Jacobi-Bellman
equation. We characterize such a property in several ways, in particular it follows that a value function which is an absolute
minimizer is a bilateral viscosity solution of the HJB equation and these two properties are often equivalent. We also determine
that bilateral solutions of HJB equations are unique among absolute minimizers with prescribed boundary conditions.
This research was partially supported by MIUR-Prin project “Metodi di viscosità, metrici e di teoria del controllo in equazioni
alle derivate parziali nonlineari”. |
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Keywords: | Degenerate elliptic equations Viscosity solutions Aronsson equation Dynamic programming method |
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