Por Jean Van Schaftingen (Université Catholique de Louvain).

Ginzburg-Landau type functionals provide a relaxation scheme to construct harmonic maps in the presence of topological obstructions. They arise in superconductivity models, in liquid crystal models (Landau-de Gennes functional) and in the generation of cross-fields in meshing. For a general compact manifold target space we describe the asymptotic number, type and location of singularities that arise in minimizers. We cover in particular the case where the fundamental group of the vacuum manifold in nonabelian and hence the singularities cannot be characterized univocally as elements of the fundamental group. We obtain similar results for \(p\)-harmonic maps with \(p\) going to \(2\).

The results unify the existing theory and cover new situations and problems.

This is a joint work with Antonin Monteil (Paris-Est Créteil, France), Rémy Rodiac (Paris-€“Saclay, France) and Benoit Van Vaerenbergh (UCLouvain).

Transmissão via Zoom.

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.