  Regularity results for minimal configurations of variational problems
involving both bulk and surface energies and subject to a volume constraint are
established. The bulk energies are convex functions with p-power growth, but
are otherwise not subjected to any further structure conditions. For a minimal
configuration (u;E), Hoelder continuity of the function u is proved as well as
partial regularity of the boundary of the minimal set E. Moreover, full
regularity of the boundary of the minimal set is obtained under suitable
closeness assumptions on the eigenvalues of the bulk energies.
