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.
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, in a unified framework, a thorough treatment of Carleman inequalities, and employs them to investigate the elliptic Cauchy problem and some classical elliptic inverse problems. ... Throughout the book, numerous particular cases and examples are provided to explain the primary results. The book is written in a clear and concise manner ... ." (Akhtar A. Khan, Mathematical Reviews, August, 2017)
"The author provides a unified approach to the study of both elliptic Cauchy problems and some elliptic inverse problems. ... This book is well written and I highly recommend it to those who are interested in inverse problems for partial differential equations." (Dinh Nho Hào, zbMATH, 1351.35260, 2017)
