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We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…

Analysis of PDEs · Mathematics 2022-04-12 Giovanni Covi , Jesse Railo , Philipp Zimmermann

We consider an inverse boundary value problem for the equation $\nabla\cdot(\sigma-i\omega\epsilon)\nabla u=0$ in a given bounded domain $\Omega$ at a fixed $\omega>0$. $\sigma$ and $\epsilon$ denote the conductivity and permittivity of the…

Analysis of PDEs · Mathematics 2021-10-01 Masaru Ikehata

We discuss the inverse problem of determining the possible presence of an (n-1)-dimensional crack \Sigma in an n-dimensional body \Omega with n > 2 when the so-called Dirichlet-to-Neumann map is given on the boundary of \Omega. In…

Analysis of PDEs · Mathematics 2014-04-07 Giovanni Alessandrini , Eva Sincich

Imposing either Dirichlet or Neumann boundary conditions on the boundary of a smooth bounded domain $\Omega$, we study the perturbation incurred by the voltage potential when the conductivity is modified in a set of small measure. We…

Analysis of PDEs · Mathematics 2021-03-18 Yves Capdeboscq , Shaun Chen Yang Ong

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…

Analysis of PDEs · Mathematics 2021-11-24 Yavar Kian , Yosra Soussi

Magneto-acousto-electric tomography (MAET) combines ultrasound with a static magnetic field to infer the electrical conductivity of an object. In this paper, we present a rigorous quasi-static mathematical model for MAET with magnetic field…

Analysis of PDEs · Mathematics 2026-03-03 Lingyun Qiu , Siqin Zheng

An inverse problem of identifying locations and certain properties of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on a part of the boundary is studied. Using as weights particular…

Mathematical Physics · Physics 2007-05-23 H. Ammari , A. G. Ramm

We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…

Analysis of PDEs · Mathematics 2024-09-05 Isaac Harris , Andreas Kleefeld , Heejin Lee

The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…

Analysis of PDEs · Mathematics 2015-06-11 Ok Kyun Lee , Hyeonbae Kang , Jong Chul Ye , Mikyoung Lim

We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…

Analysis of PDEs · Mathematics 2017-10-25 Youjun Deng , Hongyu Liu , Gunther Uhlmann

Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder\'on's method is a relatively recent EIT imaging algorithm that is…

Numerical Analysis · Mathematics 2023-11-01 Siyu Cen , Bangti Jin , Kwancheol Shin , Zhi Zhou

We construct counterexamples for the partial data inverse problem for the fractional conductivity equation in all dimensions on general bounded open sets. In particular, we show that for any bounded domain $\Omega \subset \mathbb{R}^n$ and…

Analysis of PDEs · Mathematics 2024-09-10 Jesse Railo , Philipp Zimmermann

A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…

Analysis of PDEs · Mathematics 2015-06-25 Sarah Jane Hamilton , Matti Lassas , Samuli Siltanen

The Electrical Resistance Tomography (ERT) technique is applied to the measurement of sheet conductance maps of both uniform and patterned conductive thin films. Images of the sheet conductance spatial distribution, and local conductivity…

Instrumentation and Detectors · Physics 2016-06-21 Alessandro Cultrera , Luca Callegaro

This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…

Numerical Analysis · Mathematics 2025-07-22 Kai Li , Kwancheol Shin , Zhi Zhou

In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…

Analysis of PDEs · Mathematics 2021-02-10 Isaac Harris

The inverse problem in Acousto-Electric tomography concerns the reconstruction of the electric conductivity in a domain from knowledge of the power density function in the interior of the body. This interior power density results from…

Numerical Analysis · Mathematics 2020-01-09 Changyou Li , Mirza Karamehmedovic , Ekaterina Sherina , Kim Knudsen

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…

Analysis of PDEs · Mathematics 2019-01-11 Giovanni Covi

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

Analysis of PDEs · Mathematics 2024-11-26 Mourad Choulli , Hiroshi Takase

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…

Analysis of PDEs · Mathematics 2017-01-27 Elena Beretta , Cecilia Cavaterra , Maria Cristina Cerutti , Andrea Manzoni , Luca Ratti