Geometric Conditions for Regularity of Viscosity Solution to the Simplest Hamilton-Jacobi Equation

Abstract : Continuing research in [13] and [14] on well-posedness of the optimal time control problem with a constant convex dynamics in a Hilbert space we adapt one of the regularity conditions obtained there to a slightly more general problem, where nonaffine additive term appears. We prove existence and uniqueness of a minimizer in this problem as well as continuous differentiability of the value function, which can be seen as the viscosity solution to a Hamilton-Jacobi equation, near the boundary.
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Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.245-254, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_25〉
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Vladimir Goncharov, Fátima Pereira. Geometric Conditions for Regularity of Viscosity Solution to the Simplest Hamilton-Jacobi Equation. Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.245-254, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_25〉. 〈hal-01347544〉

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