Published December 2012
| Published + Submitted
Journal Article
Open
Semi-classical analysis of the Laplace operator with Robin boundary conditions
- Creators
-
Frank, Rupert L.
- Geisinger, Leander
Chicago
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Abstract
We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove the asymptotics in terms of semi-classical analysis. In this reformulation it is natural to allow the function describing the boundary conditions to depend on the semi-classical parameter and we identify and analyze three different regimes for this dependence.
Additional Information
© 2012 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. Received: 11 August 2012. Accepted: 24 August 2012. Published online: 5 October 2012. The authors wish to thank A. Laptev for stimulating their interest in this problem. U.S. NSF grants PHY-1068285 (R.L.F.) and PHY-1122309 (L.G.) and DFG grant GE 2369/1-1 (L.G.) are acknowledged. Communicated by A. Laptev.Attached Files
Published - art_3A10.1007_2Fs13373-012-0028-5.pdf
Submitted - 1208.2327.pdf
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Additional details
- Eprint ID
- 77212
- Resolver ID
- CaltechAUTHORS:20170505-092151992
- NSF
- PHY-1068285
- NSF
- PHY-1122309
- Deutsche Forschungsgemeinschaft (DFG)
- GE 2369/1-1
- Created
-
2017-05-05Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field