On the regularization of the inverse conductivity problem with discontinuous conductivities

Luca Rondi

doi:10.3934/ipi.2008.2.397

Article Contents

2008, Volume 2, Issue 3: 397-409. Doi: 10.3934/ipi.2008.2.397

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On the regularization of the inverse conductivity problem with discontinuous conductivities

Luca Rondi^1,

1.
Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, via Valerio, 12/1, 34127 Trieste

Received: April 30, 2008

Revised: May 31, 2008

Published: July 2008

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Abstract

We consider the regularization of the inverse conductivity problem with discontinuous conductivities, like for example the so-called inclusion problem. We theoretically validate the use of some of the most widely adopted regularization operators, like for instance total variation and the Mumford-Shah functional, by proving a convergence result for the solutions to the regularized minimum problems.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 47J06, 49J45.

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