Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

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Autor/in:
Verlag/Körperschaft:
Hamburg University of Technology
Erscheinungsjahr:
2008
Medientyp:
Text
Schlagwort:
  • 510: Mathematik
Beschreibung:
  • We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form D = (x, z) ∈ Rn × R: z > f(x) where f: Rn → R is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example, acoustic scattering problems, problems involving elastic waves and problems in potential theory, have been reformulated as second kind integral equations u + Ku = v in the space BC of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator A = I + K under consideration, with an emphasis on the function space setting BC. Firstly, under which conditions is A a Fredholm operator, and, secondly, when is the finite section method applicable to A?. © 2008 Rocky Mountain Mathematics Consortium.
Beziehungen:
DOI 10.1216/JIE-2008-20-1-13
Quellsystem:
TUHH Open Research

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oai:tore.tuhh.de:11420/10578