Source supports in electrostatics

BIT Numerical Mathematics

Volumn 48, Issue 2, 2008, Pages 245-264

  Hanke, Martin ^a   Hyvönen, Nuutti ^b   Lehn, Manfred ^a   Reusswig, Stefanie ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Inverse source problem; Scattering support; Source support

Indexed keywords

EID: 49749107862     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-008-0172-1     Document Type: Article

References (18)

1. L. V. Ahlfors, Complex Analysis, 3rd edn., McGraw-Hill, New York, 1979.
2. L. Borcea, Electrical impedance tomography, Inverse Probl., 18 (2002), pp. R99-R136
3. Inverse Probl., 19 (2003), pp. 997-998.
4. M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography, Inverse Probl., 16 (2000), pp. 1029-1042.
5. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 2, Springer, Berlin, 1988.
6. A. El Badia, Inverse source problem in an anisotropic medium by boundary measurements, Inverse Probl., 21 (2005), pp. 1487-1506.
7. H. Haddar, S. Kusiak, and J. Sylvester, The convex back-scattering support, SIAM J. Appl. Math., 66 (2005), pp. 591-615.
8. M. Hämäläinen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, Magnetoencephalography - theory, instrumentation, and applications to noninvasive studies of the working human brain, Rev. Mod. Phys., 65 (1993), pp. 413-497.
9. M. Hanke, N. Hyvönen, and S. Reusswig, Convex source support and its application to electric impedance tomography, submitted.
10. P. Henrici, Applied and Computational Complex Analysis, vol. 1, Wiley, New York, 1974.
11. R. Kress, Linear Integral Equations, 2nd edn., Springer, Berlin, 1999.
12. S. Kusiak and J. Sylvester, The scattering support, Commun. Pure Appl. Math., 56 (2003), pp. 1525-1548.
13. S. Kusiak and J. Sylvester, The convex scattering support in a background medium, SIAM J. Math Anal., 36 (2005), pp. 1142-1158.
14. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, vol. I, Springer, Berlin, 1972.
15. R. Potthast, J. Sylvester, and S. Kusiak, A 'range test' for determining scatterers with unknown physical properties, Inverse Probl., 19 (2003), pp. 533-547.
16. J. Saranen and G. Vainikko, Periodic Integral and Pseudodifferential Equations with Numerical Approximation, Springer, Berlin, 2002.
17. J. Sylvester, Notions of support for far fields, Inverse Probl., 22 (2006), pp. 1273-1288.
18. J. Sylvester and J. Kelly, A scattering support for broadband sparse far field measurements, Inverse Probl., 21 (2005), pp. 759-771.