Orateur
Description
We will present variational approaches to the analysis of topological singularities in the plane, starting from the - nowadays - classical Ginzburg-Landau (GL) model and core-radius (CR) approach. We will introduce a third approach inspired by the Mumford-Shah functional used in the context of image segmentation. Within our framework, the order parameter is an SBV map taking values in the unit sphere of the plane; the bulk energy is the squared L2 norm of the approximate gradient whereas the penalization term is given by the length of the jump set, scaled by a small parameter. After providing a notion of Jacobian determinant for SBV maps, we show that at any logarithmic scale our functional is "variationally equivalent" to the "standard" (CR) and (GL) models. Joint work with Vito Crismale, Nicolas Van Goethem and Riccardo Scala.
