Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems

• Main Author: Choulli, Mourad (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Cancer research.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Physics.; Partial Differential Equations.; Mathematical Methods in Physics.; Cancer Research.; Applications of Mathematics.; Appl.Mathematics/Computational Methods of Engineering.

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 problem...

Table of Contents:

• 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.