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. © 2005 Springer Science+Business Media,Inc.
Regular solutions of Hamilton-Jacobi -Bellman equations arising in Economics
FAGGIAN, Silvia
2005-01-01
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. © 2005 Springer Science+Business Media,Inc.
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