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

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

We study the multi-channel Gel'fand-Calder\'on inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v(x) \psi = 0$, $x\in D$, where $v$ is a smooth matrix-valued potential defined on a…

Analysis of PDEs · Mathematics 2011-07-06 Roman Novikov , Matteo Santacesaria

We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…

Analysis of PDEs · Mathematics 2017-10-04 Eemeli Blåsten

We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…

Analysis of PDEs · Mathematics 2020-04-21 Giovanni S. Alberti , 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

We give effectivized Holder-logarithmic energy and regularity dependent stability estimates for the Gel'fand inverse boundary value problem in dimension $d=3$. This effectivization includes explicit dependance of the estimates on…

Analysis of PDEs · Mathematics 2015-06-19 Mikhail Isaev , Roman Novikov

This is a follow-up of a previous article where we proved local stability estimates for a potential in a Schr\"odinger equation on an open bounded set in dimension $n=3$ from the Dirichlet-to-Neumann map with partial data. The region under…

Analysis of PDEs · Mathematics 2014-05-07 David Dos Santos Ferreira , Pedro Caro , Alberto Ruiz

In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension $n \geq 3$. The stability estimates correspond to a couple of uniqueness results by Dos Santos…

Analysis of PDEs · Mathematics 2014-08-15 Pedro Caro , Mikko Salo

It is proved that, in two dimensions, the Calder\'on inverse conductivity problem in Lipschitz domains is stable in the $L^p$ sense when the conductivities are uniformly bounded in any fractional Sobolev space $W^{\alpha,p}$ $\alpha>0,…

Analysis of PDEs · Mathematics 2008-07-28 Albert Clop , Daniel Faraco , Alberto Ruiz

We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general…

Analysis of PDEs · Mathematics 2014-04-16 Giovanni Alessandrini , Kyoungsun Kim

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

Analysis of PDEs · Mathematics 2019-02-13 Hongyu Liu , Chun-Hsiang Tsou

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 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

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 show that the inverse problem of Calderon for conductivities in a two-dimensional Lipschitz domain is stable in a class of conductivities that are Dini continuous. This extends previous stability results when the conductivities are known…

Analysis of PDEs · Mathematics 2020-03-23 Robert McOwen , Bindu K Veetel

Calder\'on's inverse conductivity problem has, so far, only been subject to conditional logarithmic stability for infinite-dimensional classes of conductivities and to Lipschitz stability when restricted to finite-dimensional classes.…

Analysis of PDEs · Mathematics 2026-02-18 Henrik Garde , Markus Hirvensalo , Nuutti Hyvönen

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal…

Analysis of PDEs · Mathematics 2016-02-17 Giovanni Alessandrini , Antonino Morassi , Edi Rosset , Sergio Vessella
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