Uniqueness results for inverse Robin problems with bounded coefficient

Laurent Baratchart; Laurent Bourgeois; Juliette Leblond

doi:10.1016/j.jfa.2016.01.011

Uniqueness results for inverse Robin problems with bounded coefficient

Laurent Baratchart, Laurent Bourgeois, Juliette Leblond

INRIA

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Abstract

In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain Ω⊂Rn, with L^∞ Robin coefficient, L² Neumann data and conductivity of class W^1,r(Ω), r>n. We show that uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part, does hold in dimension n=2 but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.

Original language	English
Pages (from-to)	2508-2542
Number of pages	35
Journal	Journal of Functional Analysis
Volume	270
Issue number	7
DOIs	https://doi.org/10.1016/j.jfa.2016.01.011
Publication status	Published - 1 Apr 2016

Keywords

Elliptic regularity
Holomorphic Hardy-Smirnov classes
Robin inverse problem
Unique continuation

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title = "Uniqueness results for inverse Robin problems with bounded coefficient",

abstract = "In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain Ω⊂Rn, with L∞ Robin coefficient, L2 Neumann data and conductivity of class W1,r(Ω), r>n. We show that uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part, does hold in dimension n=2 but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.",

keywords = "Elliptic regularity, Holomorphic Hardy-Smirnov classes, Robin inverse problem, Unique continuation",

author = "Laurent Baratchart and Laurent Bourgeois and Juliette Leblond",

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AU - Bourgeois, Laurent

AU - Leblond, Juliette

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N2 - In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain Ω⊂Rn, with L∞ Robin coefficient, L2 Neumann data and conductivity of class W1,r(Ω), r>n. We show that uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part, does hold in dimension n=2 but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.

AB - In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain Ω⊂Rn, with L∞ Robin coefficient, L2 Neumann data and conductivity of class W1,r(Ω), r>n. We show that uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part, does hold in dimension n=2 but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.

KW - Elliptic regularity

KW - Holomorphic Hardy-Smirnov classes

KW - Robin inverse problem

KW - Unique continuation

U2 - 10.1016/j.jfa.2016.01.011

DO - 10.1016/j.jfa.2016.01.011

M3 - Article

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VL - 270

SP - 2508

EP - 2542

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -

Uniqueness results for inverse Robin problems with bounded coefficient

Abstract

Keywords

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