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

Appears in collection : Harmonic analysis of elliptic and parabolic partial differential equations / Analyse harmonique des équations aux dérivées partielles elliptiques et paraboliques

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.

Information about the video

Date of recording 01/05/2018
Date of publication 02/05/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19398403
Cite this video Veraar, Mark (01/05/2018). $H^\infty$-calculus and the heat equation with rough boundary conditions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19398403
URL https://dx.doi.org/10.24350/CIRM.V.19398403

Domain(s)

Bibliography

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