Karp's theorem in acoustic scattering theory

Authors:
David Colton and Andreas Kirsch

Journal:
Proc. Amer. Math. Soc. **103** (1988), 783-788

MSC:
Primary 35R30; Secondary 35J05, 35P25, 76Q05

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947658-0

MathSciNet review:
947658

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Abstract | References | Similar Articles | Additional Information

Abstract: Karp's Theorem states that if the far field pattern corresponding to the scattering of a time harmonic plane acoustic wave by a sound-soft cylinder is of the form where is the wave number, the angle of observation and the angle of incidence of the plane wave, then the cylinder must be circular. A new proof is given of this result and extended to the cases of scattering by a sound-hard obstacle and an inhomogeneous medium.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947658-0

Article copyright:
© Copyright 1988
American Mathematical Society