  We consider the vacuum energy for a scalar field subject to a frequency
dependent boundary condition. The effect of a frequency cut-off is described in
terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic
expansion for Bessel functions allows to determine the dominant (volume, area,
>...) terms in the Casimir energy. The possible interest of this kind of models
for dielectric media (and its application to sonoluminescence) is also
discussed.
