Girouard, Alexandre;
Karpukhin, Mikhail;
Levitin, Michael;
Polterovich, Iosif;
(2022)
The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript.
Journal of Spectral Theory
, 12
(1)
pp. 195-225.
10.4171/jst/399.
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Abstract
How close is the Dirichlet-to-Neumann (DtN) 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 Hörmander from the 1950s. We present Hörmander’s approach and its applications, with an emphasis on eigenvalue estimates and spectral asymptotics. In particular, we obtain results for the DtN maps on non-smooth boundaries in the Riemannian setting, the DtN operators for the Helmholtz equation and the DtN operators on differential forms.
| Type: | Article |
|---|---|
| Title: | The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/jst/399 |
| Publisher version: | https://doi.org/10.4171/jst/399 |
| Language: | English |
| Additional information: | Copyright © 2022 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10201306 |
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