Related papers: Lipschitz stability for the electrostatic inverse …
We investigate the continuity of boundary operators, such as the Neumann-to-Dirichlet map, with respect to the coefficient matrices of the underlying elliptic equations. We show that for nonsmooth coefficients the correct notion of…
We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
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…
This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the…
Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the boundary of a conductive medium (the data) are taken according to a prescribed protocol set and inverted to map the internal…
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…
We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\Omega \times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where…
We are interested in the inverse problem of the determination of the potential $p(x), x\in\Omega\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_\nu u$ on a suitable part $\Gamma_0$ of the boundary of $\Omega$,…
We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance functions from the entire space, measured on the chosen…
We consider the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material. The Lam\'e moduli of the inclusion…
We study the inverse boundary value problem of detecting a non-uniform conductivity motivated by pacing-guided ablation in cardiac electrophysiology. At the stationary level, the transmembrane potential $u$ in a region…
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…
In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…
This paper presents a mathematical framework for a flexible pressure-sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface…
In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and…
We address the stability issue in Calder\'on's problem for a special class of anisotropic conductivities of the form $\sigma=\gamma A$ in a Lipschitz domain $\Omega\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous…
We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…