A nonvariational Neumann problem for the Helmholtz equation
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913909063024640 |
|---|---|
| author | de Cristoforis, M. Lanza |
| author_facet | de Cristoforis, M. Lanza |
| contents | We consider a bounded open subset $Ω$ of ${\mathbb{R}}^n$ of class $C^{1,α}$ for some $α\in]0,1[$ and we solve the Neumann problem for the Helmholtz equation both in $Ω$ and in the exterior of $Ω$. We look for solutions in the space for $α$-Hölder continuous functions that may not have a classical normal derivative at the boundary points of $Ω$ and that may have an infinite Dirichlet integral around the boundary of $Ω$. Namely for solutions that do not belong to the classical variational setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nonvariational Neumann problem for the Helmholtz equation de Cristoforis, M. Lanza Analysis of PDEs 31B10, 35J25, 35J05 We consider a bounded open subset $Ω$ of ${\mathbb{R}}^n$ of class $C^{1,α}$ for some $α\in]0,1[$ and we solve the Neumann problem for the Helmholtz equation both in $Ω$ and in the exterior of $Ω$. We look for solutions in the space for $α$-Hölder continuous functions that may not have a classical normal derivative at the boundary points of $Ω$ and that may have an infinite Dirichlet integral around the boundary of $Ω$. Namely for solutions that do not belong to the classical variational setting. |
| title | A nonvariational Neumann problem for the Helmholtz equation |
| topic | Analysis of PDEs 31B10, 35J25, 35J05 |
| url | https://arxiv.org/abs/2504.18252 |