摘要：This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or *** surface energy is an arbitrary elliptic parametric integralwhich is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularityof the free interface of such problems.