The minimization problem for the energy functional of a two-phase medium is studied by two regularization methods. The first method uses the area of the boundary of the interface of the phases. The second one is based on the integral of the higher-order derivatives of the replacement field with nonhomogeneous boundary conditions and additional conditions on the replacement field. The existence theorem for an equilibrium state is proved in both cases. The equilibrium equation is deduced. Bibliography: 5 titles.