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Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body
Antonino Morassi, Università degli Studi di Udine, Italy, and Edi Rosset, Università degli Studi di Trieste, Italy
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Memoirs of the American Mathematical Society
2009; 58 pp; softcover
Volume: 200
ISBN-10: 0-8218-4325-7
ISBN-13: 978-0-8218-4325-3
List Price: US$57
Individual Members: US$34.20
Institutional Members: US$45.60
Order Code: MEMO/200/938
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The authors consider the inverse problem of determining a rigid inclusion inside an isotropic elastic body \(\Omega\), from a single measurement of traction and displacement taken on the boundary of \(\Omega\). For this severely ill-posed problem they prove uniqueness and a conditional stability estimate of log-log type.

Table of Contents

  • Introduction
  • Main results
  • Proof of the uniqueness result
  • Proof of the stability result
  • Proof of Proposition 4.1
  • Stability estimates of continuation from Cauchy data
  • Proof of Proposition 4.2 in the 3-D case
  • A related inverse problem in electrostatics
  • Bibliography
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