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.
Work is realized in framework of the project ”Variational Analysis: Theory and Applications” (PTDC/MAT/111809/2009) financially supported by Fundação para Ciência e Tecnologia (FCT), the Portuguese institutions COMPETE, QREN and the European Regional Development Fund (FEDER).
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Goncharov, V.V., Pereira, F.F. (2013). Geometric Conditions for Regularity of Viscosity Solution to the Simplest Hamilton-Jacobi Equation. In: Hömberg, D., Tröltzsch, F. (eds) System Modeling and Optimization. CSMO 2011. IFIP Advances in Information and Communication Technology, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36062-6_25
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DOI: https://doi.org/10.1007/978-3-642-36062-6_25
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