01205nas a2200121   4500008004300000245007700043210006900120520072500189100001900914700002500933700002200958856010300980       2015                        en_Ud  00aConstrained BV functions on double coverings for Plateau's type problems0 aConstrained BV functions on double coverings for Plateaus type p3 a<p>We link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau'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>1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio  uhttps://math.sissa.it/publication/constrained-bv-functions-double-coverings-plateaus-type-problems