IRIS PubliCatt
PubliCatt è il repository istituzionale ad accesso aperto dell'Università Cattolica del Sacro Cuore, dove gli utenti autorizzati afferenti all'Ateneo provvedono direttamente e autonomamente a depositare e a rendere visibili le proprie pubblicazioni, inserendo i dati descrittivi del documento stesso ("metadati", quali il titolo, autore, abstract, etc.) e, laddove possibile, il testo della pubblicazione stessa (full-text).
PubliCatt utilizza la piattaforma IRIS (Institutional Research Information System) sviluppata da CINECA.
EnglishWe link covering spaces with the theory of functions of bounded variation, in order to study minimal networks in the plane and Plateau's problem without fixing a priori the topology of solutions. We solve the minimization problem in the class of (possibly vector-valued) BV functions defined on a covering space of the complement of an (n -2)-dimensional compact embedded Lipschitz manifold S without boundary. This approach has several similarities with Brakke's "soap films" covering construction. The main novelty of our method stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. In the case of networks, the constraint is defined using a suitable subset of transpositions of m elements, m being the number of points of S. The model avoids all issues concerning the presence of the boundary S, which is automatically attained. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on Γ-convergence.
Amato, S., Bellettini, G., Paolini, M., Constrained BV functions on covering spaces for minimal networks and Plateau's type problems, <<ADVANCES IN CALCULUS OF VARIATIONS>>, 2017; 10 (1): 25-47. [doi:10.1515/acv-2015-0021] [http://hdl.handle.net/10807/99226]
| Autori: | ||
| Titolo: | Constrained BV functions on covering spaces for minimal networks and Plateau's type problems | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1515/acv-2015-0021 | |
| URL: | http://www.reference-global.com/loi/acv | |
| Data di pubblicazione: | 2017 | |
| Abstract: | We link covering spaces with the theory of functions of bounded variation, in order to study minimal networks in the plane and Plateau's problem without fixing a priori the topology of solutions. We solve the minimization problem in the class of (possibly vector-valued) BV functions defined on a covering space of the complement of an (n -2)-dimensional compact embedded Lipschitz manifold S without boundary. This approach has several similarities with Brakke's "soap films" covering construction. The main novelty of our method stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. In the case of networks, the constraint is defined using a suitable subset of transpositions of m elements, m being the number of points of S. The model avoids all issues concerning the presence of the boundary S, which is automatically attained. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on Γ-convergence. | |
| Lingua: | Inglese | |
| Rivista: | ||
| Citazione: | Amato, S., Bellettini, G., Paolini, M., Constrained BV functions on covering spaces for minimal networks and Plateau's type problems, <<ADVANCES IN CALCULUS OF VARIATIONS>>, 2017; 10 (1): 25-47. [doi:10.1515/acv-2015-0021] [http://hdl.handle.net/10807/99226] | |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
File in questo prodotto:
| File | Descrizione | Tipologia | Note | Licenza | |
|---|---|---|---|---|---|
| AdvCalcVar_AmatoBellPaol.pdf | Versione Editoriale (PDF) | Nessuna Nota | Non specificato | Administrator |
http://hdl.handle.net/10807/99226
Copyright © 2021