En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
1

Gradient bounds for the heat kernel on the Vicsek set

Bookmarks Report an error
Multi angle
Authors : Chen, Li (Author of the conference)
CIRM (Publisher )

Loading the player...

Abstract : In this talk, we discuss functional inequalities and gradient bounds for the heat kernel on the Vicsek set. The Vicsek set has both fractal and tree structure, whereas neither analogue of curvature nor obvious differential structure exists. We introduce Sobolev spaces in that setting and prove several characterizations based on a metric, a discretization or a weak gradient approach. We also obtain $L^{p}$ Poincaré inequalities and pointwise gradient bounds for the heat kernel. These properties have important applications in harmonic analysis like Sobolev inequalities and the Riesz transform. Moreover, several of our techniques and results apply to more general fractals and trees.

Keywords : Vicsek set; heat kernel; weak gradient; Sobolev spaces; Poincaré inequalities; p-energies

MSC Codes :
35B65 - Smoothness and regularity of solutions of PDE
46E35 - Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 10/07/2024
    Conference Date : 10/06/2024
    Subseries : Research talks
    arXiv category : Metric Geometry ; Analysis of PDEs ; Functional Analysis
    Mathematical Area(s) : Analysis and its Applications
    Format : MP4 (.mp4) - HD
    Video Time : 00:56:12
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-06-10_Chen.mp4

Information on the Event

Event Title : Harmonic analysis and partial differential equations / Analyse harmonique et équations aux dérivées partielles
Event Organizers : Bernicot, Frédéric ; Martell, José Maria ; Monniaux, Sylvie ; Portal, Pierre
Dates : 10/06/2024 - 14/06/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/2979.html

Citation Data

DOI : 10.24350/CIRM.V.20189003
Cite this video as: Chen, Li (2024). Gradient bounds for the heat kernel on the Vicsek set. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20189003
URI : http://dx.doi.org/10.24350/CIRM.V.20189003

See Also

Bibliography



Imagette Video

Bookmarks Report an error