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- W2100993614 abstract "Let Ω be a local perturbation of the n-dimensional domain Ω0 = Ropf;n − 1 × (0, π). In a previous paper8 we have introduced the notion of an admissible standing wave. We shall prove that the principle of limiting absorption holds for the Dirichlet problem of the reduced wave equation in Ω at ω ≥ 0 if Ω does not allow admissible standing waves with frequency ω. From Reference 8, this condition is satisfied for every ω ≥ 0 if Ω ≠ Ω0, and v·x′ ≤ 0 on δΩ, where x′ = (x1,…, xn − 1, 0) and v is the normal unit vector on δΩ pointing into the complement of Ω. In contrast to this, the principle of limiting absorption is violated in the case of the unperturbed domain Ω0 at the frequencies ω = 1,2,… if n ≤ 3. The second part of our investigation, which will appear in a subsequent paper, is devoted to the principle of limit amplitude." @default.
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- W2100993614 date "1988-05-01" @default.
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- W2100993614 title "On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 1: Time-independent theory" @default.
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- W2100993614 doi "https://doi.org/10.1002/mma.1670100203" @default.
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