Layer potential operators for transmission problems on extension domains

We use the well-posedness of transmission problems on classes of two-sided Sobolevextension domains to give variational definitions for (boundary) layer potential oper-ators and Neumann-Poincaré operators. These classes of domains contain Lipschitzdomains, but also domains with fractal boundaries. Our formulation does not involveany measures on the boundary. We discuss basic properties of these operators and usethem to generalize basic results in imaging beyond the Lipschitz case.