  We calculate the Casimir forces in two configurations, namely, three parallel
dielectric slabs and a dielectric slab between two perfectly conducting plates,
where the dielectric materials are dispersive and inhomogeneous in the
direction perpendicular to the interfaces. A renormalization scheme is proposed
consisting of subtracting the effect of one interface with a single
inhomogeneous medium. Some examples are worked out to illustrate this scheme.
Our method always gives finite results and is consistent with the principle of
virtual work; it extends the Dzyaloshinskii-Lifshitz-Pitaeveskii force to
inhomogeneous media.
