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In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schr\"odinger operator in dimension $n\geq 3$. We assume that the inaccessible part of the boundary is part of a…

Analysis of PDEs · Mathematics 2016-10-17 Leyter Potenciano-Machado

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Analysis of PDEs · Mathematics 2021-03-02 Peijun Li , Xiaohua Yao , Yue Zhao

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

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

Analysis of PDEs · Mathematics 2015-05-28 Kais Ammari , Mourad Choulli

This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of $\R^n$, with $n \geq 2$, we prove the stability of the first and zero order coefficients of…

Analysis of PDEs · Mathematics 2023-04-26 Nesrine Aroua , Mourad Bellassoued

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…

Analysis of PDEs · Mathematics 2019-07-23 Katya Krupchyk , Gunther Uhlmann

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 about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

Mathematical Physics · Physics 2024-01-17 Michael V. Klibanov

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

In this paper we study the inverse conductivity problem with partial data in dimension $n\geq 3$. We derive stability estimates for this inverse problem if the conductivity has $C^{1,\sigma}(\bar\Omega)\cap H^{3/2+\sigma}(\Omega)$…

Mathematical Physics · Physics 2013-08-08 Ru-Yu Lai

We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.

Analysis of PDEs · Mathematics 2013-06-27 Mikhail Isaev

We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived…

Analysis of PDEs · Mathematics 2025-11-14 Mourad Choulli , Shuai Lu , Hiroshi Takase

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 article, we prove a stability estimate going from the Radon transform of a function with limited angle-distance data to the $L^p$ norm of the function itself, under some conditions on the support of the function. We apply this…

Analysis of PDEs · Mathematics 2012-12-17 Pedro Caro , David Dos Santos Ferreira , Alberto Ruiz

In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in $\mathbb R^3$. Firstly, to connect the boundary data with the unknown source, we…

Analysis of PDEs · Mathematics 2021-02-10 Peijun Li , Xiaohua Yao , Yue Zhao

We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Neumann boundary condition in non-Lipschitz domains $\Omega \subset \mathbb C$. The suggested method is based on…

Analysis of PDEs · Mathematics 2020-01-20 Vladimir Gol'dshtein , Valerii Pchelintsev , Alexander Ukhlov

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

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that,…

Analysis of PDEs · Mathematics 2012-05-31 Habib Ammari , Hajer Bahouri , David Dos Santos Ferreira , Isabelle Gallagher

We consider the inverse problem of determining the time dependent magnetic field of the Schr\"odinger equation in a bounded open subset of $R^n$, with $n \geq 1$, from a finite number of Neumann data, when the boundary measurement is taken…

Analysis of PDEs · Mathematics 2012-09-27 Michel Cristofol , Eric Soccorsi

This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach…

Analysis of PDEs · Mathematics 2025-01-22 Xi Chen , Shuai Lu , Ruochong Zhang