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Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering
Author(s):
Plamen
Stefanov;
Gunther
Uhlmann
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1351-1354.
MSC (2000):
Primary 35R30;
Secondary 81U40, 35P25
Posted:
December 23, 2003
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Abstract:
We prove local uniqueness for the inverse problem in obstacle scattering at a fixed energy and fixed incident angle.
References:
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- [CK]
- D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin, 1998. MR 99c:35181
- [CS]
- D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering, IMA J. Appl. Math. 31(3) (1983), 253-259. MR 85e:76044
- [GT]
- D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin, 1977. MR 57:13109
- [I]
- V. Isakov, Inverse problems for partial differential equations, Appl. Math. Sci., 127, Springer-Verlag, New York, 1998. MR 99b:35211
- [KK]
- A. Kirsch and R. Kress, Uniqueness in inverse obstacle scattering, Inverse Problems 9 (1993), 285-299. MR 94e:35143
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- P. Lax and R. Phillips, Scattering Theory, Academic Press, 1967. MR 36:530
- [P]
- R. Potthast, Fréchet differentiability of boundary integral operators in inverse acoustic scattering, Inverse Problems 10 (1994), 431-447. MR 95c:35268
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Additional Information:
Plamen
Stefanov
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
stefanov@math.purdue.edu
Gunther
Uhlmann
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195
Email:
gunther@math.washington.edu
DOI:
10.1090/S0002-9939-03-07363-5
PII:
S 0002-9939(03)07363-5
Received by editor(s):
August 19, 2002
Posted:
December 23, 2003
Additional Notes:
The first author was partly supported by NSF Grant DMS-0196440 and MSRI
The second author was partly supported by NSF Grant DMS-007048 and a John Simon Guggenheim fellowship. Both authors would like to thank the hospitality of the Mathematical Sciences Research Institute where part of this work was done
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2003,
American Mathematical Society
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