  We study a variational model for soap films in which the films are
represented by sets with fixed small volume rather than surfaces. In this
problem, a minimizing sequence of completely "wet" films, or sets of finite
perimeter spanning a wire frame, may converge to a film containing both wet
regions of positive volume and collapsed (dry) surfaces. When collapsing
occurs, these limiting objects lie outside the original minimization class and
instead are admissible for a relaxed problem. Here we show that the relaxation
and the original formulation are equivalent by approximating the collapsed
films in the relaxed class by wet films in the original class.
