The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript | Vidéo | Carmin.tv

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The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript

By Iosif Polterovich

Appears in collection : Shape Optimization, Spectral Geometry and Calculus of Variations / Optimisation de forme, géométrie spectrale et calcul des variations

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

Information about the video

Date of recording 30/03/2021
Date of publication 20/04/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19738403
Cite this video Polterovich, Iosif (30/03/2021). The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19738403
URL https://dx.doi.org/10.24350/CIRM.V.19738403

Domain(s)

Spectral Theory

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

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