Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems

1. Auflage 2016
ISBN: 978-3-319-33641-1
Verlag: Springer International Publishing

Buch, Englisch, 81 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1533 g

Reihe: SpringerBriefs in Mathematics

This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. 

The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.

Zielgruppe

Research

Autoren/Hrsg.

Choulli, Mourad

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

1 Preliminaries.- 2 Uniqueness of continuation and Cauchy problems.- 3 Determining the surface impedance of an obstacle from the scattering amplitude.- 4 Determining a corrosion coecient from a boundary measurement and an attenuation coecient from an internal measurement.