# Transitions de phase et équations non locales

25-27 April 2018
Institut de mathématique Simion Stoilow de l'Académie Roumaine
Europe/Bucharest timezone

## Sur l'approximation champ de phase des problèmes variationnels faisant intervenir des ensembles connexes 1D/On a phase-field approximation of variational problems involving 1D-connected sets

25 Apr 2018, 11:30
1h

### Speaker

Antoine Lemenant (U. Paris-Diderot, France)

### Description

It is nowadays classical that phase transition models such as the Cahn-Hilliard energy can be used to regularize some more delicate functionals of geometric nature such as the Perimeter functional or more generally the $(N-1)$-Hausdorff measure. This procedure is sometimes called a Phase-Field method in numerical analysis and has been used in order to approximate some classical shape optimization problems or free discontinuity problems arising in the calculus of variations. In this talk I will present an elementary way to constraint the connectedness of the unknown set in the phase-field approach. This applies for instance to the so-called Steiner Problem, for which we indeed get a phase-field approximation, but also to other minimizing functionals on which a connectedness constraint is added. This new approach give rise to some interesting mathematical problems, both from the theoretical point of view than from the numerical one.

### Primary author

Antoine Lemenant (U. Paris-Diderot, France)

### Presentation Materials

 Transparents