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We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz…

Analysis of PDEs · Mathematics 2013-09-11 Anne-Claire Egloffe

We consider the inverse problem of determining an inclusion contained in a body for a Schr\"odinger type equation by means of local Cauchy data. Both the body and the inclusion are made by inhomogeneous and anisotropic materials. Under mild…

Analysis of PDEs · Mathematics 2024-08-08 Sonia Foschiatti , Eva Sincich

We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness…

Analysis of PDEs · Mathematics 2017-10-04 E. Blåsten , O. Yu. Imanuvilov , M. Yamamoto

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

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, we study the boundary inverse problem of determining the aligned magnetic fiaeld appearing in the magnetic Schr\"odinger equation in a periodic quantum cylindrical waveguide. Provided that the Dirichlet-to-Neumann map of…

Analysis of PDEs · Mathematics 2016-06-29 Youssef Mejri

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 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 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

This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.

Analysis of PDEs · Mathematics 2026-05-12 Tianrui Dai

We show that the spectrum of a Schr\"odinger eigenvalue problem posed on a closed Riemannian manifold $M$ with non-negative potential can be approached by that of Robin eigenvalue problems with constant positive boundary parameter posed on…

Spectral Theory · Mathematics 2024-11-05 Chia-Chun Lo

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Romina Gaburro

We study Robin-to-Robin maps, and Krein-type resolvent formulas for Schr\"odinger operators on bounded Lipschitz domains in $\bbR^n$, $n\ge 2$, with generalized Robin boundary conditions.

Analysis of PDEs · Mathematics 2008-05-15 Fritz Gesztesy , Marius Mitrea

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 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

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 consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\partial_t^2u-\Delta u+q(x)u=0$ in an unbounded…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs.…

Analysis of PDEs · Mathematics 2009-11-13 Sergio Vessella

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in…

Analysis of PDEs · Mathematics 2014-08-08 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella

In Part 1 of this paper, we have estimated the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total…

Optimization and Control · Mathematics 2018-11-15 Duong Thi Kim Huyen , Jen-Chih Yao , Nguyen Dong Yen