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This paper investigates Calder\'on's problem on a conformally transversally anisotropic manifold $ (M,g) $ of dimension $n \geq 3$, where the conductivity $ a(s,x,p) $ might depend on both the electric potential and the electric field. We…

Analysis of PDEs · Mathematics 2025-11-18 Xi Chen , Ziyun Jin

In Acousto-Electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the…

Analysis of PDEs · Mathematics 2022-07-26 Bjørn Jensen , Kim Knudsen , Hjørdis Schlüter

We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…

Analysis of PDEs · Mathematics 2019-03-27 Alexandru Tamasan , Alexander Timonov

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

Recently, a new strategy to the reconstruction of $f(R)$-gravity models based on the Raychaudhuri equation has been suggested by Choudhury et al. In this paper, utilizing this method, the reconstruction of anisotropic Einstein-Maxwell…

General Relativity and Quantum Cosmology · Physics 2020-06-24 Behzad Tajahmad

This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large…

Analysis of PDEs · Mathematics 2011-11-23 Guillaume Bal , Gunther Uhlmann

We extend monotonicity-based inversion methods to an inverse coefficient problem for the isotropic nonlocal elliptic equation \[ (-\nabla \cdot \sigma \nabla)^s u = 0 \quad \text{in } \Omega \subset \mathbb{R}^n, \] where $0 < s < 1$, $n…

Analysis of PDEs · Mathematics 2025-10-14 Yi-Hsuan Lin

We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…

Fluid Dynamics · Physics 2007-05-23 Frank Stefani , Thomas Gundrum , Gunter Gerbeth , Uwe Guenther , Mingtian Xu

We present explicit reconstruction algorithms for fully anisotropic unknown elasticity tensors from knowledge of a finite number of internal displacement fields, with applications to transient elastography. Under certain rank-maximality…

Analysis of PDEs · Mathematics 2015-07-06 Guillaume Bal , Francois Monard , Gunther Uhlmann

We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…

Analysis of PDEs · Mathematics 2016-05-09 Adrian Nachman , Alexandru Tamasan , Johann Veras

In this paper we prove uniqueness in the inverse boundary value problem for the three coefficient functions in the porous medium equation with an absorption term $\epsilon\partial_t u-\nabla\cdot(\gamma\nabla u^m)+\lambda u^q=0$, with…

Analysis of PDEs · Mathematics 2021-12-16 Cătălin I. Cârstea , Tuhin Ghosh , Gunther Uhlmann

An accurate functional inequality for Div-BV positive symmetric tensors $A$ in a bounded domain $U\subset\mathbb{R}^n$ arises whenever the tangential part of the normal trace $\gamma_\nu A\sim A\vec\nu$ is a finite measure over $\partial…

Analysis of PDEs · Mathematics 2024-12-24 Denis Serre

We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…

In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic…

Medical Physics · Physics 2024-02-01 Bjørn Jensen , Adrian Kirkeby , Kim Knudsen

This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the nonlinear reaction term $f(u)$ in a reaction-diffusion equation from overposed data. These measurements can consist of:…

Analysis of PDEs · Mathematics 2021-01-19 Barbara Kaltenbacher , William Rundell

We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…

Analysis of PDEs · Mathematics 2007-05-23 Ville Kolehmainen , Matti Lassas , Petri Ola

We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the…

Analysis of PDEs · Mathematics 2026-02-26 Yacine Mokhtari , Christina Frederick , Yunan Yang , Bjorn Engquist

We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary…

Analysis of PDEs · Mathematics 2024-05-09 Hiroshi Fujiwara , David Omogbhe , Kamran Sadiq , Alexandru Tamasan

We study inverse conductivity problem for an anisotropic conductivity in $L^\infty$ in bounded and unbounded domains. Also, we give applications of the results in the case when Dirichlet-to-Neumann and Neumann-to-Dirichlet maps are given…

Analysis of PDEs · Mathematics 2007-05-23 Kari Astala , Matti Lassas , Lassi Paivarinta

This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…

Functional Analysis · Mathematics 2015-03-06 Radu Balan