A limiting absorption principle for linear and nonlinear Helmholtz equations with a step potential
Abstract:
We consider the Helmholtz equation $-\Delta u+Vu-\lambda u=f$ on $\mathbb{R}^n$ where the potential $V:\mathbb{R}^n\to\mathbb{R}$ is constant on each of the half-spaces $\mathbb{R}^{n−1}\times(−\infty, 0)$ and $\mathbb{R}^{n−1}\times(0,\infty)$. We prove an $L^p-L^q$-Limiting Absorption Principle for frequencies $\lambda>\text{max }V$ and derive the existence of nontrivial solutions of linear and nonlinear Helmholtz equations.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2020 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000105173 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 26 S. |
| Serie | CRC 1173 Preprint ; 2020/2 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | nonlinear Helmholtz equation, limiting absorption principle, step potential |