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H 1 A critical Poincaré-Sobolev inequality

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

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    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
    47J20
    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


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