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We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a…

Mathematical Physics · Physics 2015-06-03 Horst Heck , Gen Nakamura , Haibing Wang

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…

Numerical Analysis · Mathematics 2017-04-10 Andreas Hauptmann , Matteo Santacesaria , Samuli Siltanen

We give explicit integral formulas for the solutions of planar conjugate conductivity equations in a circular domain of the right half-plane with conductivity $\sigma(x,y)=x^p$, $p\in\mathbb{Z}$. The representations are obtained via a…

Complex Variables · Mathematics 2015-04-30 Slah Chaabi , Stéphane Rigat , Franck Wielonsky

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

In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary…

Analysis of PDEs · Mathematics 2020-04-16 Isaac Harris

We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering $A_{\infty}$-measures on the boundary. More specifically, we study the…

Analysis of PDEs · Mathematics 2025-12-30 Fernando Ballesta-Yagüe , María J. Carro

We consider the Calder\'on problem with partial data in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. We show…

Analysis of PDEs · Mathematics 2016-02-16 Casey Rodriguez

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…

Analysis of PDEs · Mathematics 2019-01-15 Gen Nakamura , Manmohan Vashisth

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

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 the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…

Mathematical Physics · Physics 2021-04-05 Hannes Gernandt , Jonathan Rohleder

We consider the so called Calder\'on problem which corresponds to the determination of a conductivity appearing in an elliptic equation from boundary measurements. Using several known results we propose a simplified and self contained proof…

Analysis of PDEs · Mathematics 2019-09-20 Yavar Kian

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

Analysis of PDEs · Mathematics 2024-02-09 Yi-Hsuan Lin , Teemu Tyni , Philipp Zimmermann

We investigate the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by the stationary voltage-current (VC) map. The related inverse problem correspond to the inverse problem for the…

Analysis of PDEs · Mathematics 2021-01-25 A. Leitao

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

Analysis of PDEs · Mathematics 2016-01-21 Mourad Choulli , Yavar Kian , Eric Soccorsi

In this article, we investigate the Calder\'on problem for nonlocal parabolic equations, where we are interested to recover the leading coefficient of nonlocal parabolic operators. The main contribution is that we can relate both…

Analysis of PDEs · Mathematics 2023-08-21 Ching-Lung Lin , Yi-Hsuan Lin , Gunther Uhlmann

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

Numerical Analysis · Mathematics 2018-03-29 Antti Hannukainen , Nuutti Hyvönen , Lauri Mustonen

The problem of identifying the set of Dirichlet-to-Neumann (DtN) maps arising from conductivities on a smooth domain, among operators acting on functions on the boundary, is a challenging issue in the mathematical analysis of the Calder\'on…

Numerical Analysis · Mathematics 2026-03-17 Carlos Castro , Fabricio Macià , Cristóbal Meroño , Daniel Sánchez-Mendoza

Being motivated by the problem of deducing $L^p$-bounds on the second fundamental form of an isometric immersion from $L^p$-bounds on its mean curvature vector field, we prove a (nonlinear) Calder\'on-Zygmund inequality for maps between…

Differential Geometry · Mathematics 2018-03-08 Batu Güneysu , Stefano Pigola