Abstract
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.
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AMS subject classification (2000)
35R30, 65N21
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Hanke, M., Hyvönen, N., Lehn, M. et al. Source supports in electrostatics . Bit Numer Math 48, 245–264 (2008). https://doi.org/10.1007/s10543-008-0172-1
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DOI: https://doi.org/10.1007/s10543-008-0172-1