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We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…

Analysis of PDEs · Mathematics 2022-04-12 Giovanni Covi , Jesse Railo , Philipp Zimmermann

We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].

Analysis of PDEs · Mathematics 2011-05-17 Oleg Imanuvilov , Masahiro Yamamoto

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Romina Gaburro

This work considers properties of the Neumann-to-Dirichlet map for the conductivity equation under the assumption that the conductivity is identically one close to the boundary of the examined smooth, bounded and simply connected domain. It…

Analysis of PDEs · Mathematics 2012-04-03 Nuutti Hyvönen , Petteri Piiroinen , Otto Seiskari

In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the…

Analysis of PDEs · Mathematics 2024-11-12 Ru-Yu Lai , Gunther Uhlmann , Lili Yan

We show that measurements of the Neumann-to-Dirichlet map, roughly speaking, on a certain part of the boundary of a smooth domain in dimension 3 or higher, for inputs with support restricted to the other part, determine an electric…

Analysis of PDEs · Mathematics 2013-10-22 Francis J. Chung

We consider an inverse boundary value problem for the equation $\nabla\cdot(\sigma-i\omega\epsilon)\nabla u=0$ in a given bounded domain $\Omega$ at a fixed $\omega>0$. $\sigma$ and $\epsilon$ denote the conductivity and permittivity of the…

Analysis of PDEs · Mathematics 2021-10-01 Masaru Ikehata

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 prove that an $L^\infty$ potential in the Schr\"odinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace…

Analysis of PDEs · Mathematics 2019-10-10 Giovanni S. Alberti , Matteo Santacesaria

We consider the inverse boundary value problem of the simultaneous determination of the coefficients $\sigma$ and $q$ of the equation $-\mbox{div}(\sigma \nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given…

Analysis of PDEs · Mathematics 2025-05-26 Niall Donlon , Romina Gaburro

We study the inverse problem of determining a magnetic Schr\"odinger operator in an unbounded closed waveguide from boundary measurements. We consider this problem with a general closed waveguide in the sense that we only require our…

Analysis of PDEs · Mathematics 2019-01-29 Yavar Kian

In this paper, we consider the inverse boundary value problem of the elliptic operator $\Delta+q$ in a fixed region $\Omega\subset\mathbb{R}^3$ with unknown embedded obstacles $D$. In particular, we give a new and simple proof to uniquely…

Analysis of PDEs · Mathematics 2025-03-04 Chengyu Wu , Jiaqing Yang

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…

Analysis of PDEs · Mathematics 2010-02-16 Masaru Ikehata

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

Analysis of PDEs · Mathematics 2015-06-15 Yavar Kian , Quang Sang Phan , Eric Soccorsi

We construct counterexamples for the partial data inverse problem for the fractional conductivity equation in all dimensions on general bounded open sets. In particular, we show that for any bounded domain $\Omega \subset \mathbb{R}^n$ and…

Analysis of PDEs · Mathematics 2024-09-10 Jesse Railo , Philipp Zimmermann

We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potential over a two-plane is determined by the…

Analysis of PDEs · Mathematics 2007-05-23 Allan Greenleaf , Gunther Uhlmann

In this paper we study inverse boundary value problems with partial data for the bi-harmonic operator with first order perturbation. We consider two types of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is a…

Analysis of PDEs · Mathematics 2013-11-12 Yang Yang

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 show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations,…

Analysis of PDEs · Mathematics 2020-11-04 Yavar Kian , Katya Krupchyk , Gunther Uhlmann

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