@article {2014,
	title = {Constrained BV functions on double coverings for Plateau{\textquoteright}s type problems},
	journal = {Adv. Calc. Var.},
	year = {2015},
	abstract = {<p>We link Brakke{\textquoteright}s "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau{\textquoteright}s problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n - 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.</p>},
	author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini}
}
