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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

We study the inverse problem of determining the magnetic field and the electric potential entering the Schr\"odinger equation in an infinite 3D cylindrical domain, by Dirichlet-to-Neumann map. The cylindrical domain we consider is a closed…

Analysis of PDEs · Mathematics 2016-05-24 Mourad Bellassoued , Yavar Kian , Eric Soccorsi

We study an inverse boundary value problem with partial data in an infinite slab in $\mathbb{R}^{n}$, $n\geq 3$, for the magnetic Schr\"{o}dinger operator with an $L^{\infty}$ magnetic potential and an $L^{\infty}$ electric potential. We…

Analysis of PDEs · Mathematics 2013-11-12 Shitao Liu , Yang Yang

We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…

Analysis of PDEs · Mathematics 2023-05-09 Oleg Y. Imanuvilov , M. Yamamoto

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 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 study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and…

Analysis of PDEs · Mathematics 2015-12-01 Pedro Caro , Kaloyan Marinov

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

In this paper we consider the inverse boundary value problem for the Schr\"odinger equation with potential in $L^p$ class, $p>4/3$. We show that the potential is uniquely determined by the boundary measurements.

Analysis of PDEs · Mathematics 2017-04-24 Eemeli Blåsten , Leo Tzou , Jenn-Nan Wang

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

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

Analysis of PDEs · Mathematics 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao

We consider the inverse problems of for the fractional Schr\"odinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal…

Analysis of PDEs · Mathematics 2019-08-02 Bastian Harrach , Yi-Hsuan Lin

This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in…

Analysis of PDEs · Mathematics 2012-09-06 Valter Pohjola

The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…

Spectral Theory · Mathematics 2018-05-22 Tuncay Aktosun , Vassilis G. Papanicolaou

In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…

Analysis of PDEs · Mathematics 2026-04-09 Ravi Shankar Jaiswal , Pu-Zhao Kow , Suman Kumar Sahoo

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

This article deals with the uniqueness and stability issues in the inverse problem of determining the unbounded potential of the Schr\"odinger operator in a bounded domain of dimension 3 or greater, endowed with Robin boundary condition,…

Analysis of PDEs · Mathematics 2024-01-30 Mourad Choulli , Abdelmalek Metidji , Éric Soccorsi

We consider several inverse problems for elliptic equations whose coefficients are random, without imposing a special probabilistic structure on the randomness. The main body treats the Schr\"odinger equation. We compare what can be…

Analysis of PDEs · Mathematics 2026-05-25 Cătălin I. Cârstea

We consider, on a trivial vector bundle over a Riemannian manifold with boundary, the inverse problem of uniquely recovering time- and space-dependent coefficients of the dynamic, vector-valued Schr\"odinger equation from the knowledge of…

Analysis of PDEs · Mathematics 2021-03-16 Alexander Tetlow

The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…

Mathematical Physics · Physics 2017-08-15 Tuncay Aktosun , Ricardo Weder