Antonin Chambolle
(Ecole Polytechnique, France)
25/04/2018 09:00
We will present recent results obtained in collaboration with S. Conti (U. Bonn), G. Francfort (U. Paris-Nord), V. Crismale (E. Polytechnique, Palaiseau) and F. Iurlano (U. Pierre et Marie Curie, Paris) on the brittle fracture model of Francfort and Marigo (1998), which is a variational version of Griffith's classical model to predict crack growth. We will discuss existence of minimizers for...
Pierre bousquet
(U. Paul Sabatier Toulouse III, France)
25/04/2018 10:00
Nous considérons un problème en calcul des variations pour des fonctions définies sur un ouvert borné et à valeurs scalaires, et pour un intégrande convexe qui n'est ni régulier ni strictement convexe. Nous décrivons les propriétés de régularité et d'unicité des solutions. Il s'agit d'un travail en collaboration avec Guy Bouchitté.
We present a scalar problem in the multiple integrals...
Antoine Lemenant
(U. Paris-Diderot, France)
25/04/2018 11:30
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...
John Ball
(U. Oxford, Royaume Uni)
25/04/2018 16:30
The lecture will discuss the classical Oseen-Frank theory of nematic liquid crystals, and some results with Epifanio Virga on energy-minimizing properties of universal solutions, and with Lu Liu on exterior problems.
Didier Bresch
(CNRS Chambéry, France)
26/04/2018 09:00
The aim of this talk is to present quantitative estimates for transport
equations with rough, i.e. non-smooth, velocity fields. The final goal is to use those
estimates to obtain new global existence results à la Leray on complex systems where
the transport equations is coupled to other PDEs for instance as in fluid mechanics.
We will explain for instance how it helps to treat phase...
Armin Schikorra
(U. Pittsburgh, États-Unis)
26/04/2018 10:00
The Heisenberg groups are examples of sub-Riemannian manifolds homeomorphic, but not diffeomorphic to the Euclidean space. Their metric is derived from curves which are only allowed to move in so-called horizontal directions.
When one considers approximation or extension problems for Sobolev maps into the Riemannian manifolds it is known that topological properties of the target manifold play...
Xavier Lamy
(U. Paul Sabatier Toulouse III, France)
26/04/2018 11:30
The class of entropy solutions to the eikonal equation arises in connection with the asymptotics of the Aviles-Giga energy, a model related to smectic liquid crystals, thin film elasticity and micromagnetism. We prove, using a new simple form of the kinetic formulation, that this class coincides with the class of solutions which enjoy a certain Besov regularity.
Bernard Helffer
(U. Nantes, France)
26/04/2018 14:00
Consider a two-dimensional domain shaped like a wire, not
necessarily of uniform cross section. Let $V$ denote an electric
potential driven by a voltage drop between the conducting surfaces
of the wire. We consider the operator $A_h=-h^2\Delta+iV$ in the
semi-classical limit $h\to0$. We obtain both the asymptotic behaviour
of the left margin of the spectrum, as well as resolvent...
Radu Purice
(Institut de Mathématiques Simion Stoilow de l'Académie Roumaine, Bucarest, Roumanie)
26/04/2018 15:00
On presente des résultats obtenus en collaboration avec Horia Cornean, Bernard Helffer et Viorel Iftimie concernant l'utilisation du calcul pseudodifférentiel magnétique pour la construction des hamiltoniens effectifs de Peierls - Onsager pour l'étude des électrons dans un potentiel périodique et un champ magnétique faible et lisse.
Heiner Olbermann
(Université de Leipzig, Allemagne)
26/04/2018 16:30
We reconsider the proof of uniqueness of isometric immersions of two-dimensional spheres with positive Gauss curvature, with derivatives in a certain Hölder class. We observe that an understanding of the integrability properties of the Brouwer degree is crucial to extend the range of validity for the uniqueness statement. We take this as a motivation to state and prove a theorem about the...
Lia Bronsard
(McMaster University)
27/04/2018 09:00
We consider energy minimizing configurations of a nematic liquid crystal, as described by the Landau-de Gennes model. We focus on an important model problem concerning a nematic surrounding a spherical colloid particle, with normal anchoring at the surface. For topological reasons, the nematic director must exhibit a defect (singularity), which may take the form of a point or line defect. ...
Itai Shafrir
(Technion-Israel Institute of Technology, Israël)
27/04/2018 10:00
When $sp\ge N$ the space $W^{s,p}(S^N,S^N)$ can be decomposed into homotopy classes according to the degree of the maps. We consider two natural distances between different classes.
We prove estimates, and in some cases even explicit formulas, for these distances. Most of the work is joint with Haim Brezis (Rutgers and Technion) and Petru Mironescu (Lyon 1).
Giacomo Canevari
(Basque Center for Applied Mathematics, Bilbao, Espagne)
27/04/2018 11:30
Nematic liquid crystals are matter in an intermediate phase between the solid and the liquid ones. The constituent molecules, while isotropically distributed in space, retain long-range orientational order. The classical variational theories for nematic liquid crystals are quadratic in the gradient and as a consequence, configurations with a singular line have infinite energy within these...
Yannick Sire
(U. Johns Hopkins, États-Unis)
27/04/2018 14:00
Motivated by a conjecture of De Giorgi on the Allen-Cahn Equation and classification results for some its solutions, we will describe recent results related to one-dimensional symmetry for solutions of nonlocal equations involving possibly nonlinear nonlocal operators. We will concentrate mainly in low dimensions and present several ways to attack this problem. We will then describe open...
Mihai Mihăilescu
(U. Craiova, Roumanie)
27/04/2018 15:00
Dans cette lecture nous présentons des résultats concernant deux problèmes distincts, obtenus en collaboration avec Marian Bocea.
Premièrement, nous étudions la famille d'équations aux dérivées partielles
$-\varepsilon\Delta u-2\Delta_\infty u = 0$ ($\varepsilon >0$) dans un domaine $\Omega$ avec une condition aux limites de Dirichlet. Dans le cas où $\varepsilon = 1,$ qui est...
Vincent Millot
(U. Paris-Diderot, France)
27/04/2018 16:30
Dans cet exposé, je présenterai des résultats de régularité partielle pour les applications harmoniques fractionnaires. L’équation sous-jacente est l’analogue du système des applications harmoniques à valeurs dans une variété où le Laplacien est ici remplacé par le Laplacien fractionnaire. J’expliquerai également leur lien avec les surfaces minimales à frontière libre et les surfaces...
