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Related papers: Optimal stability estimates for a Magnetic Schr\"o…

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We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…

Analysis of PDEs · Mathematics 2024-09-10 Giovanni Covi , Jesse Railo , Teemu Tyni , Philipp Zimmermann

This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…

Analysis of PDEs · Mathematics 2023-06-21 Jian Zhai , Yue Zhao

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

In this article, high frequency stability estimates for the determination of the potential in the Schr\"odinger equation are studied when the boundary measurements are made on slightly more than half the boundary. The estimates reflect the…

Analysis of PDEs · Mathematics 2021-10-19 Anupam Pal Choudhury , Venkateswaran P. Krishnan

In this article we study stability aspects for the determination of time-dependent vector and scalar potentials in relativistic Schr\"odinger equation from partial knowledge of boundary measurements. For space dimensions strictly greater…

Analysis of PDEs · Mathematics 2020-12-30 Soumen Senapati

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

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,…

Analysis of PDEs · Mathematics 2012-11-29 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu

This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential…

Analysis of PDEs · Mathematics 2025-12-23 Yang Liu , Yixian Gao

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…

Analysis of PDEs · Mathematics 2024-05-01 Boya Liu

In this article, we study the increasing stability property for the determination of the potential in the Schr\"odinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat and homogeneous boundary…

Analysis of PDEs · Mathematics 2017-11-15 Anupam Pal Choudhury , Horst Heck

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 show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in $\R^n$, $n\ge 3$, for the magnetic Schr\"odinger operator with $L^\infty$ magnetic and electric potentials determines the magnetic field and…

Analysis of PDEs · Mathematics 2012-07-10 Katsiaryna Krupchyk , Gunther Uhlmann

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 the inverse problem of determining the time and space dependent electromagnetic potential of the Schr\"odinger equation in a bounded domain of $\mathbb R^n$, $n\geq 2$, by boundary observation of the solution over the entire…

Analysis of PDEs · Mathematics 2017-05-04 Yavar Kian , Eric Soccorsi

We consider Schr\"odinger operators on [0,\infty) with compactly supported, possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances…

Mathematical Physics · Physics 2009-08-15 Marco Marletta , Roman Shterenberg , Rudi Weikard

We examine semiclassical magnetic Schr\"{o}dinger operators with complex electric potentials. Under suitable conditions on the magnetic and electric potentials, we prove a resolvent estimate for spectral parameters in an unbounded parabolic…

Spectral Theory · Mathematics 2018-05-08 Ben Bellis

We study the inverse problem of determining a real-valued potential in the two-dimensional Schr\"odinger equation at negative energy from the Dirichlet-to-Neumann map. It is known that the problem is ill-posed and a stability estimate of…

Analysis of PDEs · Mathematics 2014-02-07 Matteo Santacesaria

We prove that the stationary magnetic potential vector and the electrostatic potential entering the dynamic magnetic Schr\"odinger equation can be Lipschitz stably retrieved through finitely many local boundary measurements of the solution.…

Analysis of PDEs · Mathematics 2018-05-28 Xinchi Huang , Yavar Kian , Eric Soccorsi , Masahiro Yamamoto

For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish H\"older type stability estimates in the geometric inverse problem of determining the electric…

Analysis of PDEs · Mathematics 2022-07-19 Victor Arnaiz , Colin Guillarmou

We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field…

Analysis of PDEs · Mathematics 2012-07-10 Katsiaryna Krupchyk , Gunther Uhlmann