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- W2001417417 abstract "The three-dimensional analog of Sommerfeld's famous half-plane problem for a screen Σ1: x1 > 0, x2 > 0, x3 = 0 is treated by an operator theoretic approach. This paper shows that the Dirichlet problem is well-posed for any complex wave-number k ∉ R, if we look for a solution u ∈ H1 (R3) of the Helmholtz equation (Δ + k2) u = 0 in e 7mid; ∑1=g ∈ H12 (∑1) with u ¦Σ1 = g ϵ H12(σ1). An explicit representation formula for the solution is established by use of general Wiener-Hopf operator theory, Sobolev space properties, and Hilbert space methods. The corresponding Neumann problem can be solved by analogy." @default.
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- W2001417417 date "1988-02-01" @default.
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- W2001417417 title "A contribution to the quarter-plane problem in diffraction theory" @default.
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- W2001417417 doi "https://doi.org/10.1016/0022-247x(88)90396-4" @default.
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