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We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…

Mathematical Physics · Physics 2013-03-12 Oleg Yu Imanuvilov , M. Yamamoto

We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…

Analysis of PDEs · Mathematics 2025-12-22 Anne-Sophie Bonnet-Ben Dhia , Lucas Chesnel , Sonia Fliss

We study the Lorentzian Calder\'on problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This…

Analysis of PDEs · Mathematics 2024-09-30 Lauri Oksanen , Rakesh , Mikko Salo

We study both the Riemannian and Lorentzian Calder\'on problem when a family of Dirichlet-to-Neumann maps are given for an open set of magnetic/electromagnetic potentials. For the Riemannian version, by allowing small perturbations of the…

Analysis of PDEs · Mathematics 2025-12-19 Yuchao Yi

We discuss a Steklov-type problem for Maxwell's equations which is related to an interior Calder\'{o}n operator and an appropriate Dirichlet-to-Neumann type map. The corresponding Neumann-to-Dirichlet map turns out to be compact and this…

Analysis of PDEs · Mathematics 2020-07-22 Pier Domenico Lamberti , Ioannis G. Stratis

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

We prove uniqueness for Calder\'on's problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and four dimensional cases, this confirms a conjecture of Uhlmann. Our proof…

Analysis of PDEs · Mathematics 2016-03-01 Pedro Caro , Keith Rogers

Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the conductivity is indeed…

Analysis of PDEs · Mathematics 2021-09-21 Felipe Ponce-Vanegas

We consider the Calder\`on problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log-log stability in the determination of the isotropic periodic conductivity coefficient from partial…

Analysis of PDEs · Mathematics 2017-11-22 Mourad Choulli , Yavar Kian , Eric Soccorsi

We consider the Calder\'on problem for systems with unknown zeroth and first order terms, and improve on previously known results. More precisely, let $(M, g)$ be a compact Riemannian manifold with boundary, let $A$ be a connection matrix…

Analysis of PDEs · Mathematics 2026-02-05 Mihajlo Cekić

We prove uniqueness of solutions to the wave map equation in the natural class, namely $ (u, \partial_t u) \in C([0,T); \dot{H}^{d/2})\times C^1([0,T); \dot{H}^{d/2-1})$ in dimensions $d\geq 4$. This is achieved through estimating the…

Analysis of PDEs · Mathematics 2011-11-21 Fabrice Planchon , Nader Masmoudi

We study inverse boundary problems for the advection diffusion equation on an admissible manifold, i.e. a compact Riemannian manifold with boundary of dimension $\ge 3$, which is conformally embedded in a product of the Euclidean real line…

Analysis of PDEs · Mathematics 2017-04-20 Katya Krupchyk , Gunther Uhlmann

The Calder\'on problem is an inverse problem with applications to electrical impedance tomography and geophysical prospection. We prove uniqueness in the Calder\'on problem in spatial dimension $n \geq 3$ for scalar conductivities in the…

Analysis of PDEs · Mathematics 2016-08-30 Clemens Bombach

We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…

Analysis of PDEs · Mathematics 2018-07-11 Monika Pichler

We study a Lorentzian version of the well-known Calder\'{o}n problem that is concerned with determination of lower order coefficients in a wave equation on a smooth Lorentzian manifold, given the associated Dirichlet-to-Neumann map. In the…

Analysis of PDEs · Mathematics 2024-04-05 Spyros Alexakis , Ali Feizmohammadi , Lauri Oksanen

On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing…

Analysis of PDEs · Mathematics 2018-09-13 Shiwu Yang , Pin Yu

We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is…

Analysis of PDEs · Mathematics 2007-05-23 Yaroslav Kurylev , Matti Lassas , Erkki Somersalo

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 consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric…

Analysis of PDEs · Mathematics 2018-03-19 Lucas Chesnel , Vincent Pagneux

We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…

Analysis of PDEs · Mathematics 2018-06-25 Monika Pichler