We consider Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space, with quadratic (respectively superquadratic) Hamiltonian and with continuous (respectively lipschitz continuous) final condition. This allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes. The results are applied to controlled heat equations.
Masiero, F. (2012). Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 32(1), 223-263 [10.3934/dcds.2012.32.223].
Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian
MASIERO, FEDERICA
2012
Abstract
We consider Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space, with quadratic (respectively superquadratic) Hamiltonian and with continuous (respectively lipschitz continuous) final condition. This allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes. The results are applied to controlled heat equations.
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