Layer potential operators for transmission problems on extension domains
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908820949696512 |
|---|---|
| author | Claret, Gabriel Hinz, Michael Rozanova-Pierrat, Anna Teplyaev, Alexander |
| author_facet | Claret, Gabriel Hinz, Michael Rozanova-Pierrat, Anna Teplyaev, Alexander |
| contents | We use the well-posedness of transmission problems on classes of two-sided Sobolev extension domains to give variational definitions for (boundary) layer potential operators and Neumann-Poincar{é} operators. These classes of domains contain Lipschitz domains, and also domains with fractal boundaries. Although our variational formulation does not involve any measures on the boundary, we recover the classical results in smooth domains by considering the surface measure on the boundary. We discuss properties of these operators and generalize basic results in imaging beyond the Lipschitz case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Layer potential operators for transmission problems on extension domains Claret, Gabriel Hinz, Michael Rozanova-Pierrat, Anna Teplyaev, Alexander Analysis of PDEs Mathematical Physics Functional Analysis We use the well-posedness of transmission problems on classes of two-sided Sobolev extension domains to give variational definitions for (boundary) layer potential operators and Neumann-Poincar{é} operators. These classes of domains contain Lipschitz domains, and also domains with fractal boundaries. Although our variational formulation does not involve any measures on the boundary, we recover the classical results in smooth domains by considering the surface measure on the boundary. We discuss properties of these operators and generalize basic results in imaging beyond the Lipschitz case. |
| title | Layer potential operators for transmission problems on extension domains |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2403.11601 |