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We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition…

Mathematical Physics · Physics 2009-11-10 Denis Borisov , Tomas Ekholm , Hynek Kovarik

This article deals with the inverse problem of determining the unbounded real-valued electric potential of the Robin Laplacian on a bounded domain of dimension 3 or greater, by incomplete knowledge of its boundary spectral data. Namely, the…

Analysis of PDEs · Mathematics 2025-07-10 Mourad Choulli , Abdelmalek Metidji , 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…

Analysis of PDEs · Mathematics 2020-07-07 Ru-Yu Lai , Ting Zhou

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in…

Analysis of PDEs · Mathematics 2013-03-01 Valter Pohjola

We consider the inverse coefficient problem of simultaneously determining the space dependent electric potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in an infinite…

Analysis of PDEs · Mathematics 2022-02-09 Mohamed Hamrouni , Imen Rassas , Éric Soccorsi

This paper is concerned with the study of inverse transmission problems for magnetic Schr\"odinger operators on bounded domains and in all of the Euclidean space, in the self-adjoint case. Assuming that the magnetic and electric potentials…

Analysis of PDEs · Mathematics 2011-12-20 Katsiaryna Krupchyk

We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater…

Analysis of PDEs · Mathematics 2023-11-09 Salem Selim , Lili Yan

We consider the Gel'fand-Calder\'on problem for a Schr\"odinger operator of the form $-(\nabla + iA)^2 + q$, defined on a ball $B$ in $\mathbb R^3$. We assume that the magnetic potential $A$ is small in $W^{s,3}$ for some $s>0$, and that…

Analysis of PDEs · Mathematics 2017-03-01 Boaz Haberman

We show that fixed energy scattering measurements for the magnetic Schroedinger operator uniquely determine the magnetic field and electric potential in dimensions $n \geq 3$. The magnetic potential, its first derivatives, and the electric…

Analysis of PDEs · Mathematics 2009-08-28 Lassi Päivärinta , Mikko Salo , Gunther Uhlmann

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 the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the…

Analysis of PDEs · Mathematics 2022-02-22 Mikko Salo , Leo Tzou

In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic…

Analysis of PDEs · Mathematics 2007-05-23 David Dos Santos Ferreira , Carlos Kenig , Johannes Sjoestrand , Gunther Uhlmann

We consider the Schr\"odinger operator $H$ with a periodic potential $p$ plus a compactly supported potential $q$ on the half-line. We prove the following results: 1) a forbidden domain for the resonances is specified, 2) asymptotics of the…

Mathematical Physics · Physics 2009-05-07 Evgeny Korotyaev

We consider an inverse spectral problem on a quantum graph associated with the square lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the Dirichlet-to-Neumann map for a boundary value…

Mathematical Physics · Physics 2023-06-26 Dongjie Wu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

In this paper, we focus on the inverse scattering problem for the nonlinear Schrodinger equation with magnetic potentials. Specifically, we investigate whether the scattering operator associated with the nonlinear Schrodinger equation can…

Analysis of PDEs · Mathematics 2025-06-03 Lei Wei , Hua Huang

We establish a global uniqueness result for an inverse boundary problem with partial data for the magnetic Schr\"odinger operator with a magnetic potential of class $W^{1,n}\cap L^\infty$, and an electric potential of class $L^n$. Our…

Analysis of PDEs · Mathematics 2022-10-14 Salem Selim

For a selfadjoint Schr\"odinger operator on the half line with a real-valued, integrable, and compactly-supported potential, it is investigated whether the boundary parameter at the origin and the potential can uniquely be determined by the…

Spectral Theory · Mathematics 2016-10-06 Tuncay Aktosun , Paul Sacks , Mehmet Unlu

In this article, we study the boundary inverse problem of determining the aligned magnetic fiaeld appearing in the magnetic Schr\"odinger equation in a periodic quantum cylindrical waveguide. Provided that the Dirichlet-to-Neumann map of…

Analysis of PDEs · Mathematics 2016-06-29 Youssef Mejri

We provide a leading order semiclassical asymptotics of the energy of bound states for magnetic Neumann Schr\"odinger operators in two dimensional (exterior) domains with smooth boundaries. The asymptotics is valid all the way up to the…

Spectral Theory · Mathematics 2014-02-26 S. Fournais , A. Kachmar

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