Galkowski, J;
Spence, EA;
(2019)
Wavenumber-Explicit Regularity Estimates on the Acoustic Single- and Double-Layer Operators.
Integral Equations and Operator Theory
, 91
, Article 6. 10.1007/s00020-019-2502-x.
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Abstract
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from L2(∂Ω)→H1(∂Ω) (where ∂Ω is the boundary of the obstacle). The new bounds are obtained using estimates on the restriction to the boundary of quasimodes of the Laplacian, building on recent work by the first author and collaborators. Our main motivation for considering these operators is that they appear in the standard second-kind boundary-integral formulations, posed in L2(∂Ω), of the exterior Dirichlet problem for the Helmholtz equation. Our new wavenumber-explicit L2(∂Ω)→H1(∂Ω) bounds can then be used in a wavenumber-explicit version of the classic compact-perturbation analysis of Galerkin discretisations of these second-kind equations; this is done in the companion paper (Galkowski, Müller, and Spence in Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem, 2017. arXiv:1608.01035).
| Type: | Article |
|---|---|
| Title: | Wavenumber-Explicit Regularity Estimates on the Acoustic Single- and Double-Layer Operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00020-019-2502-x |
| Publisher version: | https://doi.org/10.1007/s00020-019-2502-x |
| Language: | English |
| Additional information: | © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Helmholtz equation, Layer-potential operators, High frequency, Semiclassical, Boundary integral equation |
| 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.ucl.ac.uk/id/eprint/10083897 |
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