ENGLISH

Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems

By Mourad Choulli (auth.)

Book information

Publisher
Springer International Publishing
Year
2016
ISBN
978-3-319-33641-1, 978-3-319-33642-8
DOI
10.1007/978-3-319-33642-8
Language
english
Format
PDF
Filesize
1 MB (1272924 bytes)
Series
SpringerBriefs in Mathematics
Edition
1
Pages
IX, 81\88
Time added
2016-07-20 04:00:00
Partial Differential Equations; Mathematical Metho

Description

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.

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