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Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems
English
161 b
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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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