Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems

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 imped