Abstract
We study the following Helmholtz equation
\begin{equation}
(\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + \lambda u = f(x)\notag
\end{equation}
in $\Rd$ with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.
\begin{equation}
(\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + \lambda u = f(x)\notag
\end{equation}
in $\Rd$ with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.
| Original language | English |
|---|---|
| Journal | Proceedings of the Royal Society of Edinburgh. Section A, Mathematics |
| Volume | 144 |
| Issue number | 4 |
| Pages (from-to) | 857-890 |
| Number of pages | 34 |
| ISSN | 0308-2105 |
| DOIs | |
| Publication status | Published - 2014 |
| Externally published | Yes |
| MoE publication type | A1 Journal article-refereed |
Fields of Science
- 111 Mathematics
- electric potentials, magnetic potentials, Helmholtz equation, Sommerfeld condition