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H 1 $H^\infty$-calculus and the heat equation with rough boundary conditions

Auteurs : Veraar Mark (Auteur de la Conférence)
CIRM (Editeur )

Résumé : In this talk we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded $H^\infty$-calculus on weighted $L^p$-spaces for power weights which fall outside the classical class of $A_p$-weights. Furthermore, we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity. In particular, we obtain a new maximal regularity result for the heat equation with very rough inhomogeneous boundary data.
The talk is based on joint work with Nick Lindemulder.

Keywords : complex interpolation with boundary conditions; Bessel potential spaces; Sobolev spaces; pointwise multipliers; UMD; $H^\infty$-calculus; Ap-weights

Codes MSC :
42B25 - Maximal functions, Littlewood-Paley theory
46B70 - Interpolation between normed linear spaces
46E35 - Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E40 - Spaces of vector- and operator-valued functions
47A60 - Functional calculus

 Informations sur la Vidéo Langue : Anglais Date de publication : 02/05/2018 Date de captation : 01/05/2018 Collection : Research talks ; Analysis and its Applications ; Partial Differential Equations Format : MP4 Durée : 01:00:35 Domaine : Analysis and its Applications ; PDE Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2018-05-01_Veraar.mp4 Informations sur la rencontre Nom de la rencontre : Harmonic analysis of elliptic and parabolic partial differential equations / Analyse harmonique des équations aux dérivées partielles elliptiques et paraboliquesOrganisateurs de la rencontre : Monniaux, Sylvie ; Portal, PierreDates : 23/04/2018 - 27/04/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1741.htmlCitation Data DOI : 10.24350/CIRM.V.19398403 Cite this video as: Veraar Mark (2018). $H^\infty$-calculus and the heat equation with rough boundary conditions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19398403 URI : http://dx.doi.org/10.24350/CIRM.V.19398403

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Bibliographie

1. Lindemulder, N., Meyries, M., & Veraar, M. (2018). Complex interpolation with Dirichlet boundary conditions on the half line. - https://arxiv.org/abs/1705.11054

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