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＜電子ブック＞
Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems / by Mourad Choulli
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	IX, 81 p : online resource
著者標目	*Choulli, Mourad author SpringerLink (Online service)
件　名	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
一般注記	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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