Han, X;
Tacy, M;
(2015)
Sharp norm estimates of layer potentials and operators at high frequency.
Journal of Functional Analysis
, 269
(9)
pp. 2890-2926.
10.1016/j.jfa.2015.06.011.
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Abstract
In this paper, we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency λ2→∞. For single layer potentials, we find that the L2(∂Ω)→L2(Ω) norms decay in λ. The rate of decay depends on the curvature of ∂Ω: The norm is λ−3/4 in general domains and λ−5/6 if the boundary ∂Ω is curved. The double layer potential, however, displays uniform L2(∂Ω)→L2(Ω) bounds independent of curvature. By various examples, we show that all our estimates on layer potentials are sharp. The appendix by Galkowski gives bounds L2(∂Ω)→L2(∂Ω) for the single and double layer operators at high frequency that are sharp modulo logλ. In this case, both the single and double layer operator bounds depend upon the curvature of the boundary.
| Type: | Article |
|---|---|
| Title: | Sharp norm estimates of layer potentials and operators at high frequency |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jfa.2015.06.011 |
| Publisher version: | https://doi.org/10.1016/j.jfa.2015.06.011 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Layer potentials, Layer operators, High frequency, Restriction estimates |
| 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/10083919 |
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