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

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 lay...

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Bibliographic Details
Published in:Journal of functional analysis 2004-11, Vol.216 (1), p.141-171
Main Authors: Escauriaza, Luis, Mitrea, Marius
Format: Article
Language:English
Subjects:
Atomic estimates
Layer potentials
Lipschitz domains
Spectral radius
Transmission problems
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Summary: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 p 0(∂ Ω) is less than 1 2 , whenever Ω is a bounded convex domain and 1< p⩽2.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2003.12.005