Spectral gap properties of perturbed periodic media
Abstract:
We analyze periodic operators on $\mathbb{R}^n$ and small perturbations of these operators. The perturbation is periodic in $n−1$ directions and has bounded support in the remaining direction. We show that, when the perturbation has a sign, every spectral gap for the unperturbed operator is reduced by the perturbation. We develop a general theory that can be applied to elliptic operators, to systems such as that of linear elasticity, and to Maxwell’s equations.
| Zugehörige Institution(en) am KIT | Institut für Angewandte und Numerische Mathematik (IANM) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 06.2025 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000182454 |
| Verlag | KIT, Karlsruhe |
| Umfang | 29 S. |
| Serie | CRC 1173 Preprint ; 2025/26 |
| Projektinformation | SFB 1173, 258734477 (DFG, DFG KOORD, SFB 1173/3) |
| Externe Relationen | Siehe auch |
| Schlagwörter | band gap, Bloch waves, perturbation of periodic operators |
| Nachgewiesen in | OpenAlex |