  This paper deals with a family of stochastic control problems in Hilbert
spaces which arises in typical applications (such as boundary control and
control of delay equations with delay in the control) and for which is
difficult to apply the dynamic programming approach due to the unboudedness of
the control operator and to the lack of regularity of the underlying transition
semigroup. We introduce a specific concept of partial derivative, designed for
this situation, and we develop a method to prove that the associated HJB
equation has a solution with enough regularity to find optimal controls in
feedback form.
