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＜E-Book＞
Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems / by Mourad Choulli
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2016.
Publisher	Cham : Springer International Publishing : Imprint: Springer
Year	2016
Size	IX, 81 p : online resource
Authors	*Choulli, Mourad author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Mathematical physics LCSH:Cancer LCSH:Mathematics LCSH:Engineering mathematics LCSH:Engineering—Data processing FREE:Differential Equations FREE:Mathematical Methods in Physics FREE:Cancer Biology FREE:Applications of Mathematics FREE:Mathematical and Computational Engineering Applications
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-33642-8

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