Transmission problems and spectral theory for singular integral operators on Lipschitz domains
نویسندگان
چکیده
Here, ∆ is the Laplacian, μ ∈ R is a fixed parameter, ν is the outward unit normal to Ω, and Ω+ := Ω, Ω− := Rn \ Ω̄. For 1 < p < ∞, L̇p1(∂Ω) is the classical homogeneous Lp-based Sobolev spaces of order one on ∂Ω, M denotes the non-tangential maximal operator, ∂ν is the normal derivative and all restrictions to the boundary are taken in the non-tangential limit sense; detailed definitions are given in the body of the paper (cf. §2). Two closely related boundary problems are the Neumann problem and the Dirichlet problem with (maximally) regular data:
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