Singular perturbations of manifold-valued maps: topological singularities and compactness results

Session Information

Location: amf. P7 | "Gheorghe Asachi" Technical University of Iași (TUIAȘI)
Day: 4. Thursday 18
Time: 17:00-18:00
Chairperson: Ionel Dumitrel Ghiba

Presentation Details

Presentation Type: Oral presentation
Title: Singular perturbations of manifold-valued maps: topological singularities and compactness results
Abstract: Some variational models for ordered media—such as the Ginzburg–Landau model of superconductivity and the Landau–de Gennes model of liquid crystals—are based on free-energy functionals that favour configurations taking values in a given “ground-state manifold”. In this talk, we consider a simplified functional with this structure and study a singular limit in which deviations from the ground-state manifold are heavily penalised. In this regime, topological obstructions carried by the manifold may lead to the formation of singularities, whose energy diverges in the limit. Nevertheless, under suitable assumptions it is sometimes possible to prove compactness results for minimisers and/or to give a variational characterisation of the singularities that arise in this limit. The talk is based on joint work with several coauthors, including Haotong Fu and Wei Wang (Univ. Beijing), as well as Le Van Phu Cuong (Univ. Heidelberg), and Ramon Oliver Bonafoux and Giandomenico Orlandi (Univ. Verona).

Presenter

Dr Giacomo Canevari
University of Verona | Italy

Authors

1. Canevari, Giacomo | University of Verona
2. Fu, Haotong | University of Beijing
3. Wang, Wei | University of Beijing