Transmission problems and spectral theory for singular integral operators on Lipschitz domains

摘要

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K* in L-0(p)(partial derivativeOmega) is less than 1/2, whenever Omega is a bounded convex domain and 1 < p less than or equal to 2. (C) 2004 Elsevier Inc. All rights reserved.