  We study the transition from flat to wrinkled region in uniaxially stretched
thin elastic film. We set up a model variational problem, and study energy of
its ground state. Using known scaling bounds for the minimal energy, the
minimal energy can be written as a minimum of the underlying (convex) relaxed
problem plus a term, which grows linearly in the thickness of the film. We show
that in the limit of vanishing thickness the prefactor in the scaling law for
the original problem can be obtained by minimization of simpler scalar
constrained variational problems.
