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Constrained BV functions on double coverings for Plateau's type problems

TitleConstrained BV functions on double coverings for Plateau's type problems
Publication TypeJournal Article
Year of Publication2014
AuthorsAmato, S, Bellettini, G, Paolini, M
Abstract

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.

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