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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

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

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is…

Analysis of PDEs · Mathematics 2020-09-29 L. Potenciano-Machado , A. Ruiz , L. Tzou

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

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

The classical Calder\'on problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity…

Analysis of PDEs · Mathematics 2025-05-27 Giovanni Covi , Antti Kujanpää , Jesse Railo

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

Analysis of PDEs · Mathematics 2024-02-21 Katya Krupchyk , Shiqi Ma , Suman Kumar Sahoo , Mikko Salo , Simon St-Amant

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be…

Analysis of PDEs · Mathematics 2015-05-27 Katsiaryna Krupchyk , Matti Lassas , Gunther Uhlmann

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…

Analysis of PDEs · Mathematics 2024-11-26 Mourad Choulli , Hiroshi Takase

We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schr\"{o}dinger operator. This improves upon previous results of…

Analysis of PDEs · Mathematics 2014-02-19 Francis J. Chung

We study the stability issue for the inverse problem of determining a coefficient appearing in a Schr\"odinger equation defined on an infinite cylindrical waveguide. More precisely, we prove the stable recovery of some general class of…

Analysis of PDEs · Mathematics 2021-03-22 Yosra Soussi

In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…

Analysis of PDEs · Mathematics 2024-12-24 Tianjiao Wang , Xiang Xu , Yue Zhao

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

Analysis of PDEs · Mathematics 2016-09-21 Kais Ammari , Mourad Choulli , Faouzi Triki

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…

Analysis of PDEs · Mathematics 2025-07-21 Boya Liu , Hadrian Quan , Teemu Saksala , Lili Yan

We investigate recovery of the (Schr\"odinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a H\"older type stability which is a big improvement over a…

Analysis of PDEs · Mathematics 2020-08-19 Victor Isakov , Shuai Lu , Boxi Xu

We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schr{\"o}dinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data…

Analysis of PDEs · Mathematics 2015-01-09 Mourad Choulli , Yavar Kian , Eric Soccorsi

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

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 paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…

Analysis of PDEs · Mathematics 2014-07-03 Sergio Vessella

We study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that…

Analysis of PDEs · Mathematics 2017-09-13 Ibtissem Ben Aicha