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# Transitions de phase et équations non locales

25-27 avril 2018
Institut de mathématique Simion Stoilow de l'Académie Roumaine
Europe/Bucharest timezone
Accueil > Contribution List

## Liste des contributions

Affichage17 contributions sur 17
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).
Présenté par Itai SHAFRIR
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 the s ... Plus
Présenté par Antonin CHAMBOLLE
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 integra ... Plus
Présenté par Heiner OLBERMANN
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. We co ... Plus
Présenté par Lia BRONSARD
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 ... Plus
Présenté par Antoine LEMENANT
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.
Présenté par Xavier LAMY
on 25 avr. 2018 à 08:45
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 transiti ... Plus
Présenté par Didier BRESCH
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 problems ... Plus
Présenté par Yannick SIRE
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 es ... Plus
Présenté par Bernard HELFFER
Présenté par Mihai MIHĂILESCU
Présenté par Vincent MILLOT