One-day conference on Calculus of Variations - 2nd edition

Europe/Paris
Bâtiment M3 - Salle de séminaire, 3iéme étage (Laboratoire Paul Painlevé)

Bâtiment M3 - Salle de séminaire, 3iéme étage

Laboratoire Paul Painlevé

Benoît Merlet (Université de Lille), Ingrid Lacroix-Violet (Université de Lille)
Description

Aims and scope


The aim of this day is to bring together experts in Calculus of Variations with applications in different areas of physics, mechanics and image processing. 

This day features six invited plenary lectures. Limited funding for the participation of doctoral students and post-doctoral researchers is available, see below. 

 

 

Program

Confirmed Plenary speakers: 

A detailed program is available here.

 

Registration

Registrations are now opened.

 

Funding

Limited funding for the local expenses of students and young researchers is available. If you wish to apply for such support, please register and send a CV and a publication list by email to Benoît Merlet.

Participants
  • André De Laire
  • Antoine Lemenant
  • Antoine Zurek
  • Beniamin Bogosel
  • Benoit Merlet
  • Blanche Buet
  • Bouhadjar MEGUENNI
  • Caterina Calgaro
  • Frédéric Barbaresco
  • Ismail MERABET
  • Jean-François Babadjian
  • Juliette VENEL
  • Marc Pegon
  • Matthieu Bonnivard
  • Mbaye Diouf
  • Paul Pegon
  • Sahbi Keraani
  • sara kermoune
  • Thomas Rey
  • Xavier Bacon
    • 09:30 10:00
      Welcome 30m Bâtiment M3, 3ième étage, salle de convivialité

      Bâtiment M3, 3ième étage, salle de convivialité

      Laboratoire Paul Painlevé

    • 10:00 10:50
      Least gradient functions and optimal transport 50m Bâtiment M3 - Salle de séminaire, 3iéme étage

      Bâtiment M3 - Salle de séminaire, 3iéme étage

      Laboratoire Paul Painlevé

      The least gradient problem (minimizing the BV norm with given boundary data), motivated by both image processing applications and connections with minimal surfaces, is known to be equivalent, in the plane, to the Beckmann minimal-flow problem with source and target measures located on the boundary of the domain. Sobolev regularity of functions of least gradient is equivalent in this setting to L^p bounds on the solution of the Beckmann problem (i.e. on the transport density) and can be attacked with techniques which are now standard in optimal transport. From the transport point of view, the novelty of the estimates that I will present, coming from a joint paper with S. Dweik, lies in the fact they are obtained fro transport between measures which are concentrated on the boundary. From the BVpoint of view, a new result is the W^{1,p} regularity of the least gradient function whenever the boundary datum is W^{1,p} as a 1D function: moreover, the optimal transport framework is strong enough to deal with arbitrary strictly convex norms instead of the Euclidean one with almost no effort.

      Speaker: Filippo Santambrogio (Laboratoire de Mathématiques d'Orsay)
    • 10:50 11:40
      Applications s-harmoniques, régularité et singularités 50m Bâtiment M3 - Salle de séminaire, 3iéme étage

      Bâtiment M3 - Salle de séminaire, 3iéme étage

      Laboratoire Paul Painlevé

      Dans cet exposé, je présenterai des résultats de régularité partielle pour les applications s-harmoniques à valeurs dans une sphère. J’expliquerai également un résultat de classification des singularités dans le cas s=1/2, pour des applications minimisantes d’un domaine plan à valeurs dans le cercle.

      Speaker: Vincent Millot (Université Paris Diderot)
    • 11:40 12:00
      Coffee break 20m
    • 12:00 12:50
      Concentration analysis of brittle damage 50m Bâtiment M3 - Salle de séminaire, 3iéme étage

      Bâtiment M3 - Salle de séminaire, 3iéme étage

      Laboratoire Paul Painlevé

      This talk is concerned with an asymptotic analysis of a variational model of brittle damage, when the damaged zone concentrates into a set of zero Lebesgue measure, and, at the same time, the stiffness of the damaged material becomes arbitrarily small. In a particular non-trivial regime, concentration leads to a limit energy with linear growth as typically encountered in plasticity. I will show that, while the singular part of the limit energy can be easily described, the identification of the bulk part of the limit energy requires a subtler analysis of the concentration properties of the displacements. I will present a candidate bulk density that arises from a possible scenario. This is an ongoing work with J.-F. Babadjian and F. Rindler.

      Speaker: Flaviana Iurlano (Sorbonne Université)
    • 12:50 15:00
      Lunch 2h 10m Restaurant Univesitaire le Barrois (Université de Lille - FST)

      Restaurant Univesitaire le Barrois

      Université de Lille - FST

    • 15:00 15:50
      Ginzburg-Landau relaxation for harmonic maps valued into manifolds 50m Bâtiment M3 - Salle de séminaire, 3iéme étage

      Bâtiment M3 - Salle de séminaire, 3iéme étage

      Laboratoire Paul Painlevé

      Speaker: Antonin Monteil (Université catholique de Louvain)
    • 15:50 16:40
      Phase field approximation of the Steiner problem : a numerical investigation. 50m Bâtiment M3 - Salle de séminaire, 3iéme étage

      Bâtiment M3 - Salle de séminaire, 3iéme étage

      Laboratoire Paul Painlevé

      We analyze in this talk the abitity of different phase field models to approximate solutions of the Steiner problem. In particular, we will first focus on the recent phase field model introduced by
      Bonnivard, Lemenant and Santanbrogio that couples a Cahn Hilliard type functional with a penalyzed term forcing the compacness of the desired set. We then propose and justify the convergence of some slightly modified versions, which improve the regularity of its solution and use a better uniform contribution of the penalized term. In particular, we show that this phase field model are able to consider a large number of points in dimension 2 and 3.
      Finally, we also propose in comparison some numerical experiments using the approach of Chambolle, Ferrari and Merlet.

      Speaker: Elie Bretin (Institut Camille Jordan)
    • 16:40 17:30
      A «Total variation» with curvature penalization. 50m Bâtiment M3 - Salle de séminaire, 3iéme étage

      Bâtiment M3 - Salle de séminaire, 3iéme étage

      Laboratoire Paul Painlevé

      In this joint work with T. Pock (TU Graz) we propose a convex variant of the total variation which penalizes the curvature of the level lines, and is based on a Gauss map (lifting) of curves to represent curvature dependent energies as convex functionals. Applications to "image inpainting" are presented.

      Speaker: Antonin Chambolle (CMAP, Ecole Polytechnique)