Karpukhin, Mikhail;
Lagacé, Jean;
Polterovich, Iosif;
(2023)
Weyl's Law for the Steklov Problem on Surfaces with Rough Boundary.
Archive for Rational Mechanics and Analysis
, 247
, Article 77. 10.1007/s00205-023-01912-6.
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Abstract
The validity of Weyl’s law for the Steklov problem on domains with Lipschitz boundary is a well-known open question in spectral geometry. We answer this question in two dimensions and show that Weyl’s law holds for an even larger class of surfaces with rough boundaries. This class includes domains with interior cusps as well as “slow” exterior cusps. Moreover, the condition on the speed of exterior cusps cannot be improved, which makes our result, in a sense optimal. The proof is based on the methods of Suslina and Agranovich combined with some observations about the boundary behaviour of conformal mappings.
| Type: | Article |
|---|---|
| Title: | Weyl's Law for the Steklov Problem on Surfaces with Rough Boundary |
| Location: | Germany |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00205-023-01912-6 |
| Publisher version: | https://doi.org/10.1007/s00205-023-01912-6 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://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/10175885 |
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