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Recent progress in the conductivity reconstruction in Calderón’s problem
ISSN: 2773 - 4196
Publisher: author
Recent progress in the conductivity reconstruction in Calderón’s problem
Indexed in
Mathematics and Statistics
ARTICLE-FACTOR
1.3
Article Basics Score: 2
Article Transparency Score: 3
Article Operation Score: 3
Article Articles Score: 2
Article Accessibility Score: 3
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International Category Code (ICC):
ICC-1102
Publisher: Mohamed Salah Abdelouahab
International Journal Address (IAA):
IAA.ZONE/2773123584196
eISSN
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2773 - 4196
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Abstract
In this work, we study a nonlinear inverse problem for an elliptic partial differential equation known as the Calderón problem or the inverse conductivity problem. We give a short survey on the reconstruction question of conductivity from measurements on the boundary by covering the main currently known results regarding the isotropic problem with full data in two and higher dimensions. We present Nachman’s reconstruction procedure and summarize the theoretical progress of the technique to more recent results in the field. An open problem of significant interest is proposed to check whether it is possible to extend the method for Lipschitz conductivities.
