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We prove new global H\"older-logarithmic stability estimates for the near-field inverse scattering problem in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference and related stability efficiently…

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

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

The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction…

Analysis of PDEs · Mathematics 2013-06-28 Matteo Santacesaria

We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination…

Analysis of PDEs · Mathematics 2011-03-03 Roman Novikov

We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

Analysis of PDEs · Mathematics 2007-12-07 Roman Novikov

We prove a global logarithmic stability estimate for the Gel'fand-Calderon inverse problem on a two-dimensional domain.

Analysis of PDEs · Mathematics 2011-03-01 Roman Novikov , Matteo Santacesaria

We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$,…

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

We prove a new global stability estimate for the Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain or, more precisely, the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$…

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

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 [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

We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…

Analysis of PDEs · Mathematics 2023-06-13 Mourad Choulli

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

In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold $M$ with boundary from the knowledge of the boundary $\partial M,$ the Neumann eigenvalues $\lambda_j$ and…

Analysis of PDEs · Mathematics 2025-04-02 Dmitri Burago , Sergei Ivanov , Matti Lassas , Jinpeng Lu

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 consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

Analysis of PDEs · Mathematics 2022-02-09 Victor Isakov , Shuai Lu , Boxi Xu

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 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

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…

Analysis of PDEs · Mathematics 2022-03-03 Mourad Bellassoued , Houssem Haddar , Amal Labidi

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

We consider the Gel'fand inverse problem and continue studies of [Mandache,2001]. We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann map given on the energy intervals. These instability results…

Analysis of PDEs · Mathematics 2011-12-16 Mikhail Isaev
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