Hamilton Jacobi Bellman equations in infinite dimensionswith quadratic and superquadratic Hamiltonian

Federica Masiero

doi:10.3934/dcds.2012.32.223

Article Contents

2012, Volume 32, Issue 1: 223-263. Doi: 10.3934/dcds.2012.32.223

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

Federica Masiero^1,

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

Received: June 30, 2010

Revised: March 31, 2011

Published: December 2011

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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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Mathematics Subject Classification: Primary: 60H15, 93E20; Secondary: 60H10.

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