  We solve in mild sense Hamilton Jacobi Bellman equations, both in an infinite
dimensional Hilbert space and in a Banach space, with lipschitz Hamiltonian and
lipschitz continuous final condition, and asking only a weak regularizing
property on the transition semigroup of the corresponding state equation. The
results are applied to solve stochastic optimal control problems; the models we
can treat include a controlled stochastic heat equation in space dimension one
and with control and noise on a subdomain.
