Abstract
This is the first of two papers regarding a family of linear convex control problems in Hilbert spaces and the related Hamilton–Jacobi–Bellman equations. The framework is motivated by an application to boundary control of a PDE modeling investments with vintage capital. Existence and uniqueness of a strong solution (namely, the limit of classic solutions of approximating equations, introduced by Barbu and Da Prato) is investigated. Moreover, such a solution is proved to be C1 in the space variable.
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Faggian, S. Regular Solutions of First-Order Hamilton–Jacobi Equations for Boundary Control Problems and Applications to Economics. Appl Math Optim 51, 123–162 (2005). https://doi.org/10.1007/s00245-004-0809-z
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DOI: https://doi.org/10.1007/s00245-004-0809-z