Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems (SpringerBriefs in Mathematics) - Softcover

Choulli, Mourad

Softcover

ISBN 10: 331933641X ISBN 13: 9783319336411

Publisher: Springer, 2016

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2016
• Language: English
• ISBN 10: 331933641X
• ISBN 13: 9783319336411
• Binding: Paperback
• Edition number: 1
• Number of pages: 90