03389nam 22006975 450 991025407790332120251202121229.03-319-33642-810.1007/978-3-319-33642-8(CKB)3710000000721955(DE-He213)978-3-319-33642-8(MiAaPQ)EBC4538382(PPN)194379922(EXLCZ)99371000000072195520160603d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierApplications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems /by Mourad Choulli1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (IX, 81 p.)SpringerBriefs in Mathematics,2191-82013-319-33641-X Includes bibliographical references and index.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 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.SpringerBriefs in Mathematics,2191-8201Differential equationsMathematical physicsCancerMathematicsEngineering mathematicsEngineeringData processingDifferential EquationsMathematical Methods in PhysicsCancer BiologyApplications of MathematicsMathematical and Computational Engineering ApplicationsDifferential equations.Mathematical physics.Cancer.Mathematics.Engineering mathematics.EngineeringData processing.Differential Equations.Mathematical Methods in Physics.Cancer Biology.Applications of Mathematics.Mathematical and Computational Engineering Applications.515.26Choulli Mouradauthttp://id.loc.gov/vocabulary/relators/aut472386MiAaPQMiAaPQMiAaPQBOOK9910254077903321Applications of elliptic Carleman inequalities to Cauchy and inverse problems1523152UNINA