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In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

偏微分方程分析 · 数学 2012-11-29 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu

In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…

偏微分方程分析 · 数学 2014-12-04 Pedro Caro , Valter Pohjola

In this paper we study local stability estimates for a magnetic Schr\"odinger operator with partial data on an open bounded set in dimension $n\geq 3$. This is the corresponding stability estimates for the identifiability result obtained by…

偏微分方程分析 · 数学 2017-09-13 Leyter Potenciano-Machado

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

偏微分方程分析 · 数学 2019-06-05 Elena Beretta , Maarten V. de Hoop , Florian Faucher , Otmar Scherzer

We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions.…

偏微分方程分析 · 数学 2021-12-30 Mourad Choulli

We consider the problem of recovering a nonlinear potential function in a nonlinear Schr\"odinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex…

偏微分方程分析 · 数学 2023-01-20 Shuai Lu , Jian Zhai

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

偏微分方程分析 · 数学 2024-11-26 Mourad Choulli , Hiroshi Takase

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

偏微分方程分析 · 数学 2023-04-25 Xiaomeng Zhao , Ganghua Yuan

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 boundary Neumann observation of the solution. We prove H\"older stability…

偏微分方程分析 · 数学 2013-11-22 Yavar Kian , Quang Sang Phan , Eric Soccorsi

We analyze the stability of an inverse problem for determining the time-dependent matrix potential appearing in the Dirichlet initial-boundary value problem for the wave equation in an unbounded cylindrical waveguide. The observation is…

偏微分方程分析 · 数学 2024-09-04 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in…

偏微分方程分析 · 数学 2014-08-08 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella

We show that the knowledge of the Dirichlet--to--Neumann map for a nonlinear magnetic Schr\"odinger operator on the boundary of a compact complex manifold, equipped with a K\"ahler metric and admitting sufficiently many global holomorphic…

偏微分方程分析 · 数学 2021-10-28 Katya Krupchyk , Gunther Uhlmann , Lili Yan

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…

偏微分方程分析 · 数学 2012-02-27 Giovanni Alessandrini , Romina Gaburro

We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This…

偏微分方程分析 · 数学 2025-07-21 Boya Liu , Hadrian Quan , Teemu Saksala , Lili Yan

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…

偏微分方程分析 · 数学 2024-11-12 Ru-Yu Lai , Gunther Uhlmann , Lili Yan

In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely,…

偏微分方程分析 · 数学 2015-07-27 Mourad Bellassoued , Yavar Kian , Eric Soccorsi

We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $\mathbb{R}^n, n\geq2$, can uniquely determine, in a nonlinear magnetic Schr\"odinger equation, the vector-valued…

偏微分方程分析 · 数学 2020-07-07 Ru-Yu Lai , Ting Zhou

We consider the partial data inverse boundary problem for the Schr\"odinger operator at a frequency $k>0$ on a bounded domain in $\mathbb{R}^n$, $n\ge 3$, with impedance boundary conditions. Assuming that the potential is known in a…

偏微分方程分析 · 数学 2019-07-23 Katya Krupchyk , Gunther Uhlmann

In this paper, we consider the inverse boundary value problem for the polyharmonic operator. We prove that the second order perturbations are uniquely determined by the corresponding Dirichlet to Neumann map. More precisely, we show in…

偏微分方程分析 · 数学 2022-09-27 Nesrine Aroua , Mourad Bellassoued

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…

偏微分方程分析 · 数学 2025-08-15 Mihajlo Cekić , Anna Siffert