Multi angle

H 1 A critical Poincaré-Sobolev inequality

Auteurs : van den Bosch, Hanne (Auteur de la Conférence)
CIRM (Editeur )

    Loading the player...

    Résumé : We study a specific Poincaré-Sobolev inequality in bounded domains, that has recently been used to prove a semi-classical bound on the kinetic energy of fermionic many-body states. The corresponding inequality in the entire space is precisely scale invariant and this gives rise to an interesting phenomenon. Optimizers exist for some (most ?) domains and do not exist for some other domains, at least for the isosceles triangle in two dimensions. In this talk, I will discuss bounds on the constant in the inequality and the proofs of existence and non-existence.
    This is joint work with Rafael Benguria and Cristobal Vallejos (PUC, Chile)

    Keywords : Poincaré-Sobolev inequality; Gagliardo-Nirenberg-Sobolev inequality

    Codes MSC :
    35Q40 - PDEs in connection with quantum mechanics
    49J40 - Variational methods including variational inequalities
      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 26/11/2019
      Date de captation : 23/10/2019
      Collection : Research talks ; Partial Differential Equations ; Mathematical Physics
      Format : MP4
      Durée : 00:54:55
      Domaine : PDE ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-10-23_van den Bosch.mp4

    Informations sur la rencontre

    Nom de la rencontre : The Analysis of Complex Quantum Systems: Large Coulomb Systems and Related Matters / Analyse des systèmes complexes: grands systèmes coulombiens et systèmes apparentés
    Organisateurs de la rencontre : Barbaroux, Jean-Marie ; Panati, Annalisa ; Siedentop, Heinz
    Dates : 21/10/2019 - 25/10/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2066.html

    Citation Data

    DOI : 10.24350/CIRM.V.19571103
    Cite this video as: van den Bosch, Hanne (2019). A critical Poincaré-Sobolev inequality. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19571103
    URI : http://dx.doi.org/10.24350/CIRM.V.19571103

    Voir aussi


Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée