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Quantitative De Giorgi methods in kinetic theory

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Virtualconference
Auteurs : Mouhot, Clément (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : We consider hypoelliptic equations of kinetic Fokker-Planck type, also sometimes called of Kolmogorov or Langevin type, with rough coefficients in the drift-diffusion operator in velocity. We present novel short quantitative proofs of the De Giorgi intermediate-value Lemma as well as weak Harnack and Harnack inequalities (which imply Hölder continuity with quantitative estimates).
This is a joint work with Jessica Guerand.

Keywords : De Giorgi; hyperbolicity; Harnack inequality; Fokker-Planck

Codes MSC :
35B45 - A priori estimates
35B65 - Smoothness and regularity of solutions of PDE
35Q84 - Fokker-Planck equations

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Clement_MOUHOT.pdf

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 09/04/2021
    Date de captation : 23/03/2021
    Sous collection : Research talks
    arXiv category : Analysis of PDEs
    Domaine : PDE ; Analysis and its Applications ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Durée : 00:47:03
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-03-23_Mouhot.mp4

Informations sur la Rencontre

Nom de la rencontre : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse
Organisateurs de la rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine
Dates : 22/03/2021 - 26/03/2021
Année de la rencontre : 2021
URL Congrès : https://www.chairejeanmorlet.com/2355.html

Données de citation

DOI : 10.24350/CIRM.V.19735303
Citer cette vidéo: Mouhot, Clément (2021). Quantitative De Giorgi methods in kinetic theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19735303
URI : http://dx.doi.org/10.24350/CIRM.V.19735303

Voir aussi

Bibliographie

  • GUERAND, Jessica et MOUHOT, Clément. Quantitative De Giorgi methods in kinetic theory. arXiv preprint arXiv:2103.09646, 2021. - https://arxiv.org/abs/2103.09646

  • BOUIN, Emeric, DOLBEAULT, Jean, MISCHLER, Stéphane, et al. Hypocoercivity without confinement. Pure and Applied Analysis, 2020, vol. 2, no 2, p. 203-232. - https://doi.org/10.2140/paa.2020.2.203

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  • DE GIORGI, Memoria di Ennio. Sulla differenziabilitae l'analiticita delle estremali degli integrali multipli regolari. Ennio De Giorgi, 1957, p. 167. -

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  • WANG, WenDong et ZHANG, LiQun. The C α regularity of a class of non-homogeneous ultraparabolic equations. Science in China Series A: Mathematics, 2009, vol. 52, no 8, p. 1589-1606. - http://dx.doi.org/10.1007/s11425-009-0158-8

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