American Institute of Mathematical Sciences

January  2012, 32(1): 223-263. doi: 10.3934/dcds.2012.32.223

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

 1 Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy

Received  July 2010 Revised  April 2011 Published  September 2011

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.
Citation: Federica Masiero. Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 223-263. doi: 10.3934/dcds.2012.32.223
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