Year: 2022
Author: Manal Aoudj
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 1 : pp. 1–17
Abstract
We consider a nonlinear inverse problem for an elliptic partial differential equation known as the Calderόn problem or the inverse conductivity problem. Based on several results, we briefly summarize them to motivate this research field. We give a general view of the problem by reviewing the available results for $C^2$ conductivities. After reducing the original problem to the inverse problem for a Schrödinger equation, we apply complex geometrical optics solutions to show its uniqueness. After extending the ideas of the uniqueness proof result, we establish a stable dependence between the conductivity and the boundary measurements. By using the Carleman estimate, we discuss the partial data problem, which deals with measurements that are taken only in a part of the boundary.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.1
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 1 : pp. 1–17
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Calderόn problem Inverse conductivity problem Dirichlet-to-Neumann map Complex geometrical optics solutions Carleman estimate.