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The aim of the paper is twofold. Firstly, we would like to derive quantitative uniqueness estimates for solutions of the general complex conductivity equation. It is still unknown whether the \emph{strong} unique continuation property holds…

Analysis of PDEs · Mathematics 2018-10-02 Catalin Carstea , Tu Nguyen , Jenn-Nan Wang

We prove that the Dirichlet-to-Neumann map of the linear wave equation determines the topological, differentiable and conformal structure of the underlying Lorentzian manifold, under mild technical assumptions. With more stringent geometric…

Analysis of PDEs · Mathematics 2023-10-30 Alberto Enciso , Michał Wrochna , Gunther Uhlmann

We show in two dimensions that measuring Dirichlet data for the conductivity equation on an open subset of the boundary and, roughly speaking, Neumann data in slightly larger set than the complement uniquely determines the conductivity on a…

Analysis of PDEs · Mathematics 2008-09-19 Oleg Yu. Imanuvilov , Gunther Uhlmann , masahiro Yamamoto

We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…

Mathematical Physics · Physics 2020-07-14 Christian Daveau , Abdessatar Khelifi , Houssem Lihiou

This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…

Numerical Analysis · Mathematics 2022-08-25 Angel A. Ciarbonetti , Sergio Idelsohn , Ruben D. Spies

We study the uniqueness question for two inverse problems on graphs. Both problems consist in finding (possibly complex) edge or nodal based quantities from boundary measurements of solutions to the Dirichlet problem associated with a…

Combinatorics · Mathematics 2015-10-13 Justin Boyer , Jack J. Garzella , Fernando Guevara Vasquez

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…

Analysis of PDEs · Mathematics 2021-11-24 Jianli Xiang , Guanghui Hu

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…

Analysis of PDEs · Mathematics 2014-04-07 Giovanni Alessandrini , Eva Sincich

This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…

Analysis of PDEs · Mathematics 2022-03-01 Xiaoxu Xu , Guanghui Hu , Bo Zhang , Haiwen Zhang

We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by…

Analysis of PDEs · Mathematics 2016-02-24 Kari Astala , Matti Lassas , Lassi Paivarinta

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…

Analysis of PDEs · Mathematics 2011-06-22 Mikko Salo , Xiao Zhong

We extend a global uniqueness result for the Calder\'on problem with partial data, due to Kenig-Sj\"ostrand-Uhlmann, to the case of less regular conductivities. Specifically, we show that in dimensions $n\ge 3$, the knowledge of the…

Analysis of PDEs · Mathematics 2016-06-22 Katya Krupchyk , Gunther Uhlmann

We use X^{s,b}-inspired spaces to prove a uniqueness result for Calderon's problem in a Lipschitz domain under the assumption that the conductivity is Lipschitz. For Lipschitz conductivities, we obtain uniqueness for conductivities close to…

Analysis of PDEs · Mathematics 2019-12-19 Boaz Haberman , Daniel Tataru

This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.

Analysis of PDEs · Mathematics 2026-05-12 Tianrui Dai

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 extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Amp\`ere equation \[ \det D^2 u = F. \] We prove that, on a convex Euclidean domain in the…

Analysis of PDEs · Mathematics 2025-10-14 Tony Liimatainen , Yi-Hsuan Lin

In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

Analysis of PDEs · Mathematics 2019-11-14 Suman Kumar Sahoo , Manmohan Vashisth

The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…

Analysis of PDEs · Mathematics 2025-08-15 Mihajlo Cekić , Anna Siffert

In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the…

Differential Geometry · Mathematics 2015-07-28 Arif Amirov , Fikret Gölgeleyen , Masahiro Yamamoto