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Ausstrahlungsproblem des Laplace-Operators für eine Klasse der Gebiete mit unbeschränktem Rand

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Abstract

In this paper we prove the existence and uniqueness of a solution u satisfying the equation-Δ u − k2 y = f (k ∈ ℝ, k ≠ 0), homogeneous Dirichlet data on the boundary and a radiation condition at infinity. We consider this problem in some unbounded region with an infinite boundary for which the assumption ν(x) · σ(x) ≦0 holds; here ν denotes the exterior normal and σ a given field.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Jyväskylä, Sammonkatu 6, SF-40100, Jyväskylä 10, Finland

    Jukka Saranen

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  1. Jukka Saranen
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Saranen, J. Ausstrahlungsproblem des Laplace-Operators für eine Klasse der Gebiete mit unbeschränktem Rand. Manuscripta Math 20, 355–376 (1977). https://doi.org/10.1007/BF01171127

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  • DOI: https://doi.org/10.1007/BF01171127

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