Determination of a linear crack in an elastic body from boundary measurements-lipschitz stability

Elena Beretta; Elisa Francini; Sergio Vessella

doi:10.1137/070698397

Determination of a linear crack in an elastic body from boundary measurements-lipschitz stability

Elena Beretta, Elisa Francini, Sergio Vessella

Mathematics

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

Abstract

We discuss the stability issue for the problem of determining a thin inclusion in a homogeneous isotropic elastic body from boundary measurements. This problem is severely ill-posed, but in this paper we prove that by restricting ourselves to the class of thin neighborhoods of line segments, a Lipschitz stability estimate holds

Original language	English (US)
Pages (from-to)	984-1002
Number of pages	19
Journal	SIAM Journal on Mathematical Analysis
Volume	40
Issue number	3
DOIs	https://doi.org/10.1137/070698397
State	Published - Sep 2008

Keywords

Cracks
Inverse problems
Linear elasticity

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/070698397

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title = "Determination of a linear crack in an elastic body from boundary measurements-lipschitz stability",

abstract = "We discuss the stability issue for the problem of determining a thin inclusion in a homogeneous isotropic elastic body from boundary measurements. This problem is severely ill-posed, but in this paper we prove that by restricting ourselves to the class of thin neighborhoods of line segments, a Lipschitz stability estimate holds",

keywords = "Cracks, Inverse problems, Linear elasticity",

author = "Elena Beretta and Elisa Francini and Sergio Vessella",

year = "2008",

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language = "English (US)",

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AU - Francini, Elisa

AU - Vessella, Sergio

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N2 - We discuss the stability issue for the problem of determining a thin inclusion in a homogeneous isotropic elastic body from boundary measurements. This problem is severely ill-posed, but in this paper we prove that by restricting ourselves to the class of thin neighborhoods of line segments, a Lipschitz stability estimate holds

AB - We discuss the stability issue for the problem of determining a thin inclusion in a homogeneous isotropic elastic body from boundary measurements. This problem is severely ill-posed, but in this paper we prove that by restricting ourselves to the class of thin neighborhoods of line segments, a Lipschitz stability estimate holds

KW - Cracks

KW - Inverse problems

KW - Linear elasticity

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JF - SIAM Journal on Mathematical Analysis

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Determination of a linear crack in an elastic body from boundary measurements-lipschitz stability

Abstract

Keywords

ASJC Scopus subject areas

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