We prove that the inverse problem of determining unknown defects of various types in a conductor by performing electrostatic measurements at the boundary is severely ill-posed. We show that the ill-posedness does not depend on the nature of the defects to be determined and, more importantly, by the kind, choice and number of measurements performed.

Exponential instability for inverse elliptic problems with unknown boundaries / M. DI CRISTO, L. Rondi. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6596. - 73:1(2007), pp. 012005.1-012005.18. [10.1088/1742-6596/73/1/012005]

Exponential instability for inverse elliptic problems with unknown boundaries

M. DI CRISTO;L. Rondi
2007

Abstract

We prove that the inverse problem of determining unknown defects of various types in a conductor by performing electrostatic measurements at the boundary is severely ill-posed. We show that the ill-posedness does not depend on the nature of the defects to be determined and, more importantly, by the kind, choice and number of measurements performed.
inverse boundary value problems; instability
Settore MAT/05 - Analisi Matematica
2007
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/658512
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