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H 1 Sharp inequalities for solutions to elliptic problems with mixed boundary conditions

Auteurs : Trombetti, Cristina (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on L1 comparison) between solutions to an elliptic partial differential equation on a smooth bounded set Ω with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as Ω. This includes for instance mixed problems.

    Keywords : a priori estimates; comparison principle; mixed boundary conditions; Robin boundary conditions

    Codes MSC :
    35B45 - A priori estimates
    35J05 - Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
    35B06 - Symmetries, invariants, etc. in context of PDE


      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 20/04/2021
      Date de captation : 02/04/2021
      Sous collection : Research talks
      Format : MP4
      arXiv category : Analysis of PDEs
      Domaine : PDE
      Durée : 00:44:44
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2021-04-02_Trombetti.mp4

    Informations sur la Rencontre Virtuelle

    Nom de la rencontre : Shape Optimization, Spectral Geometry and Calculus of Variations / Optimisation de forme, géométrie spectrale et calcul des variations
    Organisateurs de la rencontre : Bucur, Dorin ; Fragalà, Ilaria ; Henrot, Antoine
    Dates : 29/03/2021 - 02/04/2021
    Année de la rencontre : 2021
    URL Congrès : https://conferences.cirm-math.fr/2299.html

    Citation Data

    DOI : 10.24350/CIRM.V.19738503
    Cite this video as: Trombetti, Cristina (2021). Sharp inequalities for solutions to elliptic problems with mixed boundary conditions.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19738503
    URI : http://dx.doi.org/10.24350/CIRM.V.19738503


    Voir aussi

    Bibliographie

    1. ALVINO, A., CHIACCHIO, F., NITSCH, C., et al. Sharp estimates for solutions to elliptic problems with mixed boundary conditions. Journal de Mathématiques Pures et Appliquées, 2020. - https://doi.org/10.1016/j.matpur.2020.12.003

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