Karp's Theorem in Inverse Obstacle Scattering Problems
DOI:
https://doi.org/10.24297/jam.v17i0.8399Keywords:
Inverse obstacle scattering problem, Karp's Theorem, Symmetric problemAbstract
In this work, we provide a proof of the so-called Karp's theorem in a different approach. We use the unique continuation principle together with the monotonicity of eigenvalues for the negative Laplace operator. This method is new and would be applicable to other types of inverse scattering problems.
Downloads
References
David Colton and Rainer Kress. Inverse acoustic and electromagnetic scattering theory, volume 93 of Applied
Mathematical Sciences. Springer, New York, third edition, 2013.
Alexander G. Ramm. Scattering by obstacles, volume 21 of Mathematics and its Applications. D. Reidel Publishing
Co., Dordrecht, 1986.
David Colton and Rainer Kress. Looking back on inverse scattering theory. SIAM Rev., 60(4):779{807, 2018.
Samuel N. Karp. Far eld amplitudes and inverse diraction theory. In Electromagnetic waves, pages 291{300.
Univ. of Wisconsin Press, Madison, Wis., 1962.
David Colton and Andreas Kirsch. Karp's theorem in acoustic scattering theory. Proc. Amer. Math. Soc.,
(3):783{788, 1988.
David Colton and Rainer Kress. Karp's theorem in electromagnetic scattering theory. Proc. Amer. Math. Soc.,
(3):764{769, 1988.
P. A. Martin and G. Dassios. Karp's theorem in elastodynamic inverse scattering. Inverse Problems, 9(1):97{111,
Alexander G. Ramm. Symmetry properties of scattering amplitudes and applications to inverse problems. J.
Math. Anal. Appl., 156(2):333{340, 1991.
Alexander G. Ramm. Symmetry problem. Proc. Amer. Math. Soc., 141(2):515{521, 2013.
Alexander G. Ramm. Symmetry problems for the Helmholtz equation. Appl. Math. Lett., 96:122{125, 2019.
Fioralba Cakoni and David Colton. A Qualitative Approach to Inverse Scattering Theory. Applied Mathematical
Sciences. Springer US, 2013.
Rolf Leis. Initial boundary value problems in mathematical physics. Teubner, 1986.
L. E. Payne and H. F. Weinberger. An optimal Poincare inequality for convex domains. Arch. Rational Mech.
Anal., 5:286{292 (1960), 1960.
Downloads
Published
How to Cite
Issue
Section
License
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.