EAN: 9783319336411

SPRINGERBRIEFS IN MATHEMATICS APPLICATIONS OF...

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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