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

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• 作者：Escauriaza ; Luis ; Mitrea ; Marius
• 关键词：35J25 ; 58J32 ; 31B10 ; 31B15 ; 31A10 ; 45B05 ; 47G10 ; 78A30 ; Transmission problems ; Lipschitz domains ; Layer potentials ; Atomic estimates ; Spectral radius
• 刊名：Journal of Functional Analysis
• 出版年：2004
• 出版时间：November 1, 2004
• 年：2004
• 卷：216
• 期：1
• 页码：141-171
• 全文大小：378 K

文摘

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^p₀(∂Ω) is less than , whenever Ω is a bounded convex domain and 1<p≤2.