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 vectors.The 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.
