Layer potential operators for transmission problems on extension domains
Résumé
We use the well-posedness of transmission problems on classes of two-sided Sobolev
extension domains to give variational definitions for (boundary) layer potential oper-
ators and Neumann-Poincaré operators. These classes of domains contain Lipschitz
domains, but also domains with fractal boundaries. Our formulation does not involve
any measures on the boundary. We discuss basic properties of these operators and use
them to generalize basic results in imaging beyond the Lipschitz case.
Mots clés
Fractal boundaries Layer potentials Poincaré-Steklov operator Neumann-Poincaré operator Calderón projector elliptic transmission problems inverse problems
Fractal boundaries
Layer potentials
Poincaré-Steklov operator
Neumann-Poincaré operator
Calderón projector
elliptic transmission problems
inverse problems
| Origine | Fichiers produits par l'(les) auteur(s) |
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