✦ LIBER ✦
On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces
✍ Scribed by David Colton; Rainer Kress
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 119 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.277
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✦ Synopsis
Abstract
Let D⊂ℝ^3^ be a bounded domain with connected boundary δD of class C^2^. It is shown that Herglotz wave functions are dense in the space of solutions to the Helmholtz equation with respect to the norm in H^1^(D) and that the electric fields of electromagnetic Herglotz pairs are dense in the space of solutions to curl curl E=k^2^E with respect to the norm in H~curl~(D). Two proofs are given in each case, one based on the denseness of the traces of Herglotz wave functions on δD and the other on variational methods. Copyright © 2001 John Wiley & Sons, Ltd.