Topological singularities for vector-valued Sobolev maps and applications

Giacomo Canevari; Giandomenico Orlandi

doi:10.5802/afst.1677

Topological singularities for vector-valued Sobolev maps and applications
[Singularités topologiques des fonctions de Sobolev à valeurs vectorielles et applications]

Giacomo Canevari ¹ ; Giandomenico Orlandi ¹

¹ Università di Verona, Dipartimento di Informatica, Strada le Grazie 15, 37134 Verona (Italy)

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 2, pp. 327-351.

Résumé
Abstract

Nous passons en revue certains résultats d’analyse des singularités topologiques des fonctions de Sobolev à valeurs dans des variétés, ainsi que leurs applications aux problèmes variationnels de type Ginzburg–Landau et au problème du relèvement dans l’espace BV. En particulier, nous présentons des résultats récents, portant sur les fonctions à valeurs vectorielles, qui trouvent leur application dans l’étude des modèles variationnels pour la science des matériaux, tels que le modèle de Landau–de Gennes.

We review the analysis of topological singularities of Sobolev maps into manifolds and their applications to variational problems of Ginzburg–Landau type and to the lifting problem for BV maps into manifolds. We describe in particular recent results obtained in the vector-valued case related to variational models of material science, more precisely the Landau–de Gennes model.

Publié le : 2021-07-09

DOI : 10.5802/afst.1677

Classification : 58C06, 49Q15, 49Q20
Keywords: Topological singularities, Flat chains, Ginzburg–Landau type functionals, Manifold-valued maps, Lifting problem
Mot clés : Singularités topologiques, Chaînes bémol, Fonctionnelles de type Ginzburg–Landau, Applications à valeurs dans des variétés, Problème du relèvement

Affiliations des auteurs :

Giacomo Canevari ¹ ; Giandomenico Orlandi ¹

¹ Università di Verona, Dipartimento di Informatica, Strada le Grazie 15, 37134 Verona (Italy)

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Giacomo Canevari; Giandomenico Orlandi. Topological singularities for vector-valued Sobolev maps and applications. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 2, pp. 327-351. doi : 10.5802/afst.1677. https://afst.centre-mersenne.org/articles/10.5802/afst.1677/

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