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The Helmholtz equation in disturbed half‐spaces
Author(s) -
Willers A.,
Werner P.
Publication year - 1987
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670090124
Subject(s) - mathematics , helmholtz equation , mathematical analysis , operator (biology) , electric field integral equation , plane (geometry) , boundary (topology) , boundary value problem , integral equation , field (mathematics) , pure mathematics , geometry , biochemistry , chemistry , repressor , transcription factor , gene
We consider boundary value problems for the Helmholtz equation in domains with boundaries coinciding with a plane outside a sufficiently large sphere. As opposed to the method of Gartmeier [6] (see also [12]) our analysis leads to an integral equation of the second kind with a compact operator. In the last chapter we study the set of far field patterns which are generated by entire incident fields.