Source supports in electrostatics
We investigate the inverse source problem of electrostatics in a bounded and convex domain with compactly supported source. We try to extract all information about the unknown source support from the given Cauchy data of the associated potential, adopting by this previous work of Kusiak and Sylvester to the case of electrostatics. We introduce, and for the unit disk we also compute numerically, what we call the discoidal source support, i.e., the smallest set made up by the intersection of disks within the domain, which carries a source compatible with the given data.
Key wordsinverse source problem scattering support source support
Unable to display preview. Download preview PDF.
- 2.L. Borcea, Electrical impedance tomography, Inverse Probl., 18 (2002), pp. R99–R136, and Inverse Probl., 19 (2003), pp. 997–998.Google Scholar
- 4.R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 2, Springer, Berlin, 1988.Google Scholar
- 8.M. Hanke, N. Hyvönen, and S. Reusswig, Convex source support and its application to electric impedance tomography, submitted.Google Scholar
- 9.P. Henrici, Applied and Computational Complex Analysis, vol. 1, Wiley, New York, 1974.Google Scholar
- 13.J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, vol. I, Springer, Berlin, 1972.Google Scholar