Determining an anisotropic conductivity by boundary measurements: Stability at the boundary

Giovanni Alessandrini; Romina Gaburro; Eva Sincich

doi:10.1016/j.jde.2023.11.001

Determining an anisotropic conductivity by boundary measurements: Stability at the boundary

Giovanni Alessandrini
, Romina Gaburro
, Eva Sincich

University of Trieste

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body Ω⊂Rⁿ, n≥3, by means of the so-called local Neumann-to-Dirichlet map on a curved portion Σ of its boundary ∂Ω. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in Inverse Problems 33 (2018), 125013, we provide a Hölder stability estimate on Σ when the conductivity is a-priori known to be a constant matrix near Σ.

Original language	English
Pages (from-to)	115-140
Number of pages	26
Journal	Journal of Differential Equations
Volume	382
DOIs	https://doi.org/10.1016/j.jde.2023.11.001
Publication status	Published - 15 Feb 2024

Keywords

Anisotropic conductivities
Calderón problem
Stability at the boundary

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10.1016/j.jde.2023.11.001

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abstract = "We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body Ω⊂Rn, n≥3, by means of the so-called local Neumann-to-Dirichlet map on a curved portion Σ of its boundary ∂Ω. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in Inverse Problems 33 (2018), 125013, we provide a H{\"o}lder stability estimate on Σ when the conductivity is a-priori known to be a constant matrix near Σ.",

keywords = "Anisotropic conductivities, Calder{\'o}n problem, Stability at the boundary",

author = "Giovanni Alessandrini and Romina Gaburro and Eva Sincich",

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AU - Gaburro, Romina

AU - Sincich, Eva

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Y1 - 2024/2/15

N2 - We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body Ω⊂Rn, n≥3, by means of the so-called local Neumann-to-Dirichlet map on a curved portion Σ of its boundary ∂Ω. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in Inverse Problems 33 (2018), 125013, we provide a Hölder stability estimate on Σ when the conductivity is a-priori known to be a constant matrix near Σ.

AB - We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body Ω⊂Rn, n≥3, by means of the so-called local Neumann-to-Dirichlet map on a curved portion Σ of its boundary ∂Ω. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in Inverse Problems 33 (2018), 125013, we provide a Hölder stability estimate on Σ when the conductivity is a-priori known to be a constant matrix near Σ.

KW - Anisotropic conductivities

KW - Calderón problem

KW - Stability at the boundary

UR - https://www.scopus.com/pages/publications/85177078689

U2 - 10.1016/j.jde.2023.11.001

DO - 10.1016/j.jde.2023.11.001

M3 - Article

AN - SCOPUS:85177078689

SN - 0022-0396

VL - 382

SP - 115

EP - 140

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Determining an anisotropic conductivity by boundary measurements: Stability at the boundary

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Keywords

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