Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.07411 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915101126164480 |
|---|---|
| author | Cañizares, Manuel |
| author_facet | Cañizares, Manuel |
| contents | We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with respect to boundary deformation, and we illustrate how to find a domain in which the Neumann problem can be solved for any energy, if there is some freedom in the choice of the domain. This work is motivated by a Runge approximation result in the context of an inverse problem in point-source scattering with partial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary deformation techniques for Neumann problems for the Helmholtz equation Cañizares, Manuel Analysis of PDEs Mathematical Physics 35R30, 49R05, 49Q10 We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with respect to boundary deformation, and we illustrate how to find a domain in which the Neumann problem can be solved for any energy, if there is some freedom in the choice of the domain. This work is motivated by a Runge approximation result in the context of an inverse problem in point-source scattering with partial data. |
| title | Boundary deformation techniques for Neumann problems for the Helmholtz equation |
| topic | Analysis of PDEs Mathematical Physics 35R30, 49R05, 49Q10 |
| url | https://arxiv.org/abs/2501.07411 |