Abstract
This paper concerns the characterization of the value function associated with a state constrained Bolza problem in which the data are allowed to be discontinuous w.r.t. the time variable on a set of zero measure and have everywhere left and right limits. Using techniques coming from viability theory and nonsmooth analysis, we provide a characterization of the value function as the unique solution to the Hamilton-Jacobi equation, in a generalized sense which employs the lower Dini derivative and the proximal normal vectors.
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Bernis, J., Bettiol, P. (2020). Solutions to the Hamilton-Jacobi Equation for Bolza Problems with State Constraints and Discontinuous Time Dependent Data. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science(), vol 11958. Springer, Cham. https://doi.org/10.1007/978-3-030-41032-2_3
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DOI: https://doi.org/10.1007/978-3-030-41032-2_3
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