Electrical impedance tomography and Calderón's problem

G Uhlmann - Inverse problems, 2009 - iopscience.iop.org
We survey mathematical developments in the inverse method of electrical impedance
tomography which consists in determining the electrical properties of a medium by making …

Inverse problems: seeing the unseen

G Uhlmann - Bulletin of Mathematical Sciences, 2014 - Springer
This survey article deals mainly with two inverse problems and the relation between them.
The first inverse problem we consider is whether one can determine the electrical …

The Calderón problem in transversally anisotropic geometries

DDS Ferreira, Y Kurylev, M Lassas, M Salo - Journal of the European …, 2016 - ems.press
We consider the anisotropic Calderón problem of recovering a conductivity matrix or a
Riemannian metric from electrical boundary measurements in three and higher dimensions …

The Calderón problem with partial data on manifolds and applications

C Kenig, M Salo - Analysis & PDE, 2014 - msp.org
We consider Calderón's inverse problem with partial data in dimensions n≥ 3. If the
inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction …

Recent progress in the Calderón problem with partial data

C Kenig, M Salo - Contemp. Math, 2014 - books.google.com
Recent progress in the Calderón problem with partial data Page 202 Contemporary
Mathematics Volume 615 , 2014 http://dx. doi. org/10.1090/conm/615/12245 Recent …

Monotonicity-based inversion of the fractional Schrödinger equation I. Positive potentials

B Harrach, YH Lin - SIAM Journal on Mathematical Analysis, 2019 - SIAM
We consider an inverse problem for the fractional Schrödinger equation by using
monotonicity formulas. We provide if-and-only-if monotonicity relations between positive …

The attenuated ray transform on simple surfaces

M Salo, G Uhlmann - Journal of differential geometry, 2011 - projecteuclid.org
THE ATTENUATED RAY TRANSFORM ON SIMPLE SURFACES Mikko Salo & Gunther
Uhlmann Abstract 1. Introduction The geodesic ray trans Page 1 j. differential geometry 88 (2011) …

Momentum ray transforms and a partial data inverse problem for a polyharmonic operator

S Bhattacharyya, VP Krishnan, SK Sahoo - SIAM Journal on Mathematical …, 2023 - SIAM
We study an inverse problem involving the unique recovery of lower order anisotropic tensor
perturbations of a polyharmonic operator in a bounded domain from the knowledge of the …

Unique determination of anisotropic perturbations of a polyharmonic operator from partial boundary data

S Bhattacharyya, VP Krishnan, SK Sahoo - arxiv preprint arxiv …, 2021 - arxiv.org
We study an inverse problem involving the unique recovery of several lower order
anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the …

Ground States of Time-Harmonic Semilinear Maxwell Equations in with Vanishing Permittivity

J Mederski - Archive for Rational Mechanics and Analysis, 2015 - Springer
We investigate the existence of solutions E: R^ 3 → R^ 3 E: R 3→ R 3 of the time-harmonic
semilinear Maxwell equation ∇ * (∇ * E)+ V (x) E=\partial_E F (x, E)\rm in R^ 3∇×(∇× E)+ V …