03694nam 22006735 450 991025407790332120220329215435.03-319-33642-810.1007/978-3-319-33642-8(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,2191-81983-319-33641-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,2191-8198Partial differential equationsPhysicsCancer researchApplied mathematicsEngineering mathematicsPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Cancer Researchhttps://scigraph.springernature.com/ontologies/product-market-codes/B11001Applications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Mathematical and Computational Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T11006Partial differential equations.Physics.Cancer research.Applied mathematics.Engineering mathematics.Partial Differential Equations.Mathematical Methods in Physics.Cancer Research.Applications of Mathematics.Mathematical and Computational Engineering.515.26Choulli Mouradauthttp://id.loc.gov/vocabulary/relators/aut472386MiAaPQMiAaPQMiAaPQBOOK9910254077903321Applications of elliptic Carleman inequalities to Cauchy and inverse problems1523152UNINA