Layer potential operators for transmission problems on extension domains
Analysis of PDEs
2026-02-10 v4 Mathematical Physics
Functional Analysis
math.MP
Abstract
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{\'e} 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.
Cite
@article{arxiv.2403.11601,
title = {Layer potential operators for transmission problems on extension domains},
author = {Gabriel Claret and Michael Hinz and Anna Rozanova-Pierrat and Alexander Teplyaev},
journal= {arXiv preprint arXiv:2403.11601},
year = {2026}
}