English
Related papers

Related papers: Reconstruction of non-self-adjoint anisotropic and…

200 papers

We extend the monotonicity method for direct exact reconstruction of inclusions in the partial data Calder\'on problem, to the case of general anisotropic conductivities in any spatial dimension $d\geq 2$. From a local Neumann-to-Dirichlet…

Analysis of PDEs · Mathematics 2025-12-02 Henrik Garde , David Johansson , Thanasis Zacharopoulos

We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calder\'on's problem. In a previous result by the authors on monotonicity-based reconstruction, the perturbed coefficient is…

Analysis of PDEs · Mathematics 2022-08-24 Henrik Garde , Nuutti Hyvönen

In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet map. Only…

Analysis of PDEs · Mathematics 2018-12-20 Henrik Garde , Stratos Staboulis

We are concerned with the Calder\'on inverse inclusion problem, where one intends to recover the shape of an inhomogeneous conductive inclusion embedded in a homogeneous conductivity by the associated boundary measurements. We consider the…

Analysis of PDEs · Mathematics 2021-05-26 Hongyu Liu , Chun-Hsiang Tsou , Wei Yang

This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…

Analysis of PDEs · Mathematics 2020-08-18 Henrik Garde

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

Analysis of PDEs · Mathematics 2019-02-13 Hongyu Liu , Chun-Hsiang Tsou

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…

Analysis of PDEs · Mathematics 2014-05-13 David Dos Santos Ferreira , Yaroslav Kurylev , Matti Lassas , Mikko Salo

The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…

Analysis of PDEs · Mathematics 2021-02-05 Valentina Candiani , Jérémi Dardé , Henrik Garde , Nuutti Hyvönen

We show that there is generically non-uniqueness for the anisotropic Calder\'on problem at fixed frequency when the Dirichlet and Neumann data are measured on disjoint sets of the boundary of a given domain. More precisely, we first show…

Analysis of PDEs · Mathematics 2017-06-28 Thierry Daudé , Niky Kamran , Francois Nicoleau

A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…

Numerical Analysis · Mathematics 2020-07-20 Rashmi Murthy , Yi-Hsuan Lin , Kwancheol Shin , Jennifer L. Mueller

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…

Machine Learning · Computer Science 2023-09-29 Jérôme Bolte , Edouard Pauwels , Antonio Silveti-Falls

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

We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map…

Analysis of PDEs · Mathematics 2020-12-08 Yi-Hsuan Lin

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

Spectral Theory · Mathematics 2012-05-22 Jussi Behrndt , Jonathan Rohleder

The inverse problem of linear elasticity is to determine the Lam\'e parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the resulting displacements on its boundary. This work…

Analysis of PDEs · Mathematics 2026-01-23 Sarah Eberle-Blick , Henrik Garde , Nuutti Hyvönen

We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull…

Analysis of PDEs · Mathematics 2015-03-17 Tommi Brander , Manas Kar , Mikko Salo

We consider the problem of reconstructing inhomogeneities in an isotropic elastic body using time harmonic waves. Here we extend the so called monotonicity method for inclusion detection and show how to determine certain types of…

Analysis of PDEs · Mathematics 2023-09-18 Sarah Eberle-Blick , Valter Pohjola

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 knowledge of the Dirichlet to Neumann map on a part of boundary. The…

Analysis of PDEs · Mathematics 2021-11-16 Sombuddha Bhattacharyya , Venkateswaran P. Krishnan , Suman Kumar Sahoo

The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the field of inverse problems, because of its fundamental role in…

In this paper we study an inverse problem for fractional anisotropic conductivity. Our nonlocal operator is based on the well-developed theory of nonlocal vector calculus, and differs substantially from other generalizations of the…

Analysis of PDEs · Mathematics 2022-12-23 Giovanni Covi
‹ Prev 1 2 3 10 Next ›