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The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript
Virtualconference
Authors : Polterovich, Iosif (Author of the conference)
CIRM (Publisher )
35P20 - Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
58J50 - Spectral problems; spectral geometry; scattering theory
CIRM (Publisher )
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Abstract :
How close is the Dirichlet-to-Neumann map to the square root of the corresponding boundary Laplacian? This question has been actively investigated in recent years. Somewhat surprisingly, a lot of techniques involved can be traced back to a newly rediscovered manuscript of Lars Hörmander from the 1950s. We present Hörmander's approach and its applications, with an emphasis on eigenvalue estimates and spectral asymptotics. The talk is based on a joint work with Alexandre Girouard, Mikhail Karpukhin and Michael Levitin
Keywords : Dirichlet-to-Neumann map; Laplace operator; Steklov eigenvalues; eigenvalue asymptotics
MSC Codes : Keywords : Dirichlet-to-Neumann map; Laplace operator; Steklov eigenvalues; eigenvalue asymptotics
35P20 - Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
58J50 - Spectral problems; spectral geometry; scattering theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/04/2021 Conference Date : 30/03/2021 Subseries : Research talks arXiv category : Spectral Theory Mathematical Area(s) : PDE ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:50:09 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-30_Polterovich.mp4 
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Information on the Event
Event Title : Shape Optimization, Spectral Geometry and Calculus of Variations / Optimisation de forme, géométrie spectrale et calcul des variationsEvent Organizers : Bucur, Dorin ; Fragalà, Ilaria ; Henrot, Antoine Dates : 29/03/2021 - 02/04/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2299.html
Citation Data
DOI : 10.24350/CIRM.V.19738403Cite this video as: Polterovich, Iosif (2021). The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19738403 URI : http://dx.doi.org/10.24350/CIRM.V.19738403 |
See Also
- [Virtualconference] Sharp inequalities for solutions to elliptic problems with mixed boundary conditions / Author of the conference Trombetti, Cristina.
- [Virtualconference] Spectrum of the Möbius strip: true, fake and not-so-fake / Author of the conference Krejcirik, David.
- [Virtualconference] Upper and lower bounds for some shape functionals / Author of the conference Buttazzo, Giuseppe.
Bibliography
- GIROUARD, Alexandre, KARPUKHIN, Mikhail, LEVITIN, Michael, et al. The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript. arXiv preprint arXiv:2102.06594, 2021. - https://arxiv.org/abs/2102.06594
