The inverse conductivity problem via the calculus of functions of bounded variation

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV functions. The space of the functions of bounded variation is recommended here as the most appropr...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 43; no. 8; pp. 5032 - 5072
Main Authors: Charalambopoulos, Antonios, Markaki, Vanessa, Kourounis, Drosos
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30.05.2020
Subjects:
boundary value problems for second‐order elliptic equations
Calculus of variations
Conductivity
Functionals
inverse problems
Mathematical analysis
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV functions. The space of the functions of bounded variation is recommended here as the most appropriate functional space hosting the conductivity profile under reconstruction. For the numerical investigation of the inversion of the inclusion problem, we propose and implement a suitable minimization scheme of an enriched—constructed herein—functional, by exploiting the inner structure of BV space. Finally, we validate and illustrate our theoretical results with numerical experiments.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6251