On Aronsson Equation and Deterministic Optimal Control

Journal Article · Wed Apr 15 00:00:00 EDT 2009 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-008-9048-7· OSTI ID:21241865

Soravia, Pierpaolo ^[1]

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1. Universita di Padova, Dipartimento di Matematica Pura e Applicata (Italy)

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.

• OSTI ID: 21241865
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 59; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
FUNCTIONS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL
VISCOSITY