IRIS Institutional Research Information System - AIR Archivio Istituzionale della Ricerca

IRIS è il sistema di gestione integrata dei dati della ricerca (persone, progetti, pubblicazioni, attività) adottato dall'Università degli Studi di Milano.

AIR nasce in UNIMI nel 2006 con lo scopo di raccogliere, documentare e conservare le informazioni sulla produzione scientifica dell'Università degli Studi di Milano e costituisce di fatto l'Anagrafe della ricerca dell'Ateneo.

We consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We aim to reconstruct the defects by performing measurements of current and voltage type on a (known and accessible) part of the boundary of the conductor. A crucial step in this reconstruction is the determination of the electrostatic potential inside the conductor, by the electrostatic boundary measurements performed. Since the defects are unknown, we state such a determination problem as a free-discontinuity problem for the electrostatic potential in the framework of special functions of bounded variation. We provide a characterisation of the looked for electrostatic potential and we approximate it with the minimum points of a sequence of functionals, which take also in account the error in the measurements. These functionals are related to the so-called Mumford-Shah functional, which acts as a regularizing term and allows us to prove existence of minimizers and Gamma-convergence properties.

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