Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering

Authors:
Plamen Stefanov and Gunther Uhlmann

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1351-1354

MSC (2000):
Primary 35R30; Secondary 81U40, 35P25

DOI:
https://doi.org/10.1090/S0002-9939-03-07363-5

Published electronically:
December 23, 2003

MathSciNet review:
2053339

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove local uniqueness for the inverse problem in obstacle scattering at a fixed energy and fixed incident angle.

**[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****[LP]**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:
https://doi.org/10.1090/S0002-9939-03-07363-5

Received by editor(s):
August 19, 2002

Published electronically:
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

Article copyright:
© Copyright 2003
American Mathematical Society