Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: The case of non-flat interfaces

Elena Beretta; Elisa Francini; Antonino Morassi; Edi Rosset; Sergio Vessella

doi:10.1088/0266-5611/30/12/125005

Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: The case of non-flat interfaces

Elena Beretta, Elisa Francini, Antonino Morassi, Edi Rosset, Sergio Vessella

Mathematics

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

Abstract

We consider the inverse problem of determining the Lamé moduli for a piecewise constant elasticity tensor = ∑_j _j?Dj, where {D_j} is a known finite partition of the body ω, from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates can be derived under C^1,?regularity assumptions on the interfaces.

Original language	English (US)
Article number	125005
Journal	Inverse Problems
Volume	30
Issue number	12
DOIs	https://doi.org/10.1088/0266-5611/30/12/125005
State	Published - Dec 1 2014

Keywords

Lamé system
Lipschitz stability 1. Introduction
inverse boundary value problem
piecewise constant coefficients

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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10.1088/0266-5611/30/12/125005

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abstract = "We consider the inverse problem of determining the Lam{\'e} moduli for a piecewise constant elasticity tensor = ∑j j?Dj, where {Dj} is a known finite partition of the body ω, from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates can be derived under C1,?regularity assumptions on the interfaces.",

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author = "Elena Beretta and Elisa Francini and Antonino Morassi and Edi Rosset and Sergio Vessella",

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AU - Beretta, Elena

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AU - Morassi, Antonino

AU - Rosset, Edi

AU - Vessella, Sergio

PY - 2014/12/1

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N2 - We consider the inverse problem of determining the Lamé moduli for a piecewise constant elasticity tensor = ∑j j?Dj, where {Dj} is a known finite partition of the body ω, from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates can be derived under C1,?regularity assumptions on the interfaces.

AB - We consider the inverse problem of determining the Lamé moduli for a piecewise constant elasticity tensor = ∑j j?Dj, where {Dj} is a known finite partition of the body ω, from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates can be derived under C1,?regularity assumptions on the interfaces.

KW - Lamé system

KW - Lipschitz stability 1. Introduction

KW - inverse boundary value problem

KW - piecewise constant coefficients

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Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: The case of non-flat interfaces

Abstract

Keywords

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