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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.12306 |
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| _version_ | 1866913237187952640 |
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| author | Ströher, Eric |
| author_facet | Ströher, Eric |
| contents | We study the electric Helmholtz equation $Δu + Vu + λu =f$ and show that, for certain potentials, the solution $u$ given by the limited absorption principle obeys a Sommerfeld radiation condition. We use a non-spherical approach based on the solution $K$ of the eikonal equation $|\nabla K|^2=1 + \frac{p}λ$ to improve previous results in that area and extend them to long-range potentials which decay like $|x|^{-2-α}$ at infinity, with $α> 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sommerfeld Radiation Condition for Helmholtz Equations with long-range Potentials Ströher, Eric Analysis of PDEs 35B25 (Primary) 35J05 (Secondary) We study the electric Helmholtz equation $Δu + Vu + λu =f$ and show that, for certain potentials, the solution $u$ given by the limited absorption principle obeys a Sommerfeld radiation condition. We use a non-spherical approach based on the solution $K$ of the eikonal equation $|\nabla K|^2=1 + \frac{p}λ$ to improve previous results in that area and extend them to long-range potentials which decay like $|x|^{-2-α}$ at infinity, with $α> 0$. |
| title | Sommerfeld Radiation Condition for Helmholtz Equations with long-range Potentials |
| topic | Analysis of PDEs 35B25 (Primary) 35J05 (Secondary) |
| url | https://arxiv.org/abs/2402.12306 |