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Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…

Analysis of PDEs · Mathematics 2015-06-17 Guillaume Bal , Cédric Bellis , Sébastien Imperiale , François Monard

We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…

Analysis of PDEs · Mathematics 2019-08-20 Guillaume Bal , François Monard

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data…

Mathematical Physics · Physics 2016-02-17 Carlos Montalto , Alexandru Tamasan

We consider the inverse problem of determining the unknown function $\alpha: \mathbb{R} \rightarrow \mathbb{R}$ from the DN map associated to the operator $\mbox{div}(A(x',\alpha (x\_3))\nabla \cdot)$ acting in the infinite straight…

Analysis of PDEs · Mathematics 2015-01-08 Mourad Choulli , Eric Soccorsi

This paper concerns the reconstruction of a scalar diffusion coefficient $\sigma(x)$ from redundant functionals of the form $H_i(x)=\sigma^{2\alpha}(x)|\nabla u_i|^2(x)$ where $\alpha\in\Rm$ and $u_i$ is a solution of the elliptic problem…

Analysis of PDEs · Mathematics 2012-04-24 Francois Monard , Guillaume Bal

We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calder\'on Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are…

Analysis of PDEs · Mathematics 2022-02-03 Daniel Faraco , Martí Prats

We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…

Differential Geometry · Mathematics 2025-05-01 Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas , Anthony Várilly-Alvarado

We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open…

Analysis of PDEs · Mathematics 2019-10-18 Ravi Shankar

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…

Numerical Analysis · Mathematics 2017-12-21 Larisa Beilina , Kati Niinimäki

The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the…

Functional Analysis · Mathematics 2023-10-12 Mikko Salo , Hjørdis Schlüter

We study the local recovery of an unknown piecewise constant anisotropic conductivity in EIT (electric impedance tomography) on certain bounded Lipschitz domains $\Omega$ in $\mathbb{R}^2$ with corners. The measurement is conducted on a…

Analysis of PDEs · Mathematics 2023-02-01 Maarten V. de Hoop , Takashi Furuya , Ching-Lung Lin , Gen Nakamura , Manmohan Vashisth

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

We prove a global uniqueness result for the Calder\'{o}n inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of…

Analysis of PDEs · Mathematics 2023-05-10 Cătălin I. Cârstea , Ali Feizmohammadi , Yavar Kian , Katya Krupchyk , Gunther Uhlmann

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

Analysis of PDEs · Mathematics 2025-12-08 Henrik Garde

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $\Sigma$ of the…

Analysis of PDEs · Mathematics 2017-12-06 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by…

Analysis of PDEs · Mathematics 2017-11-22 Ru-Yu Lai , Ravi Shankar , Daniel Spirn , Gunther Uhlmann

The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…

Mathematical Physics · Physics 2013-02-27 Martin Norgren

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Romina Gaburro

In this paper, we address a particular case of Calder\'on's (or conductivity) inverse problem in dimension two, namely the case of a homogeneous background containing a finite number of cavities (i.e. heterogeneities of infinitely high…

Analysis of PDEs · Mathematics 2018-03-12 Alexandre Munnier , Karim Ramdani