Constrained BV functions on double coverings for Plateau's type problems
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Amato, Stefano | |
| dc.contributor.author | Bellettini, Giovanni | |
| dc.contributor.author | Paolini, Maurizio | |
| dc.date.accessioned | 2015-03-09T09:51:42Z | |
| dc.date.available | 2015-03-09T09:51:42Z | |
| dc.date.issued | 2014 | |
| dc.description.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. | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/34452 | |
| dc.language.iso | en_US | en_US |
| dc.subject | double coverings | en_US |
| dc.subject | Plateau's problem | en_US |
| dc.subject | constrained BV functions | en_US |
| dc.title | Constrained BV functions on double coverings for Plateau's type problems | en_US |
| dc.type | Preprint | en_US |