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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the commutative properties of boundary integral operators


Author: G. F. Roach
Journal: Proc. Amer. Math. Soc. 73 (1979), 219-227
MSC: Primary 35C15; Secondary 35J05, 45E05
MathSciNet review: 516468
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Abstract: A discussion of the interior Dirichlet and Neumann problems of classical potential theory can be given in terms of the symmeterisers of certain related integral operators. Recent developments in the theory and application of integral equations of the first kind have made this approach towards the solution of boundary value problems a more attractive proposition. However for problems more general than those arising in potential theory a greater knowledge of associated spectral properties is required together with a realisation that much of the symmetry occurring in potential problems will be lost and that attention must be directed instead towards commutativity relations. This is demonstrated by considering boundary value problems associated with the Helmholtz equation.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0516468-5
PII: S 0002-9939(1979)0516468-5
Keywords: Boundary integral operators
Article copyright: © Copyright 1979 American Mathematical Society