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010   $a3-319-33642-8
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035   $a(DE-He213)978-3-319-33642-8
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035   $a(PPN)194379922
035   $a(EXLCZ)993710000000721955
100   $a20160603d2016      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aApplications of elliptic Carleman inequalities to Cauchy and inverse problems /$fby Mourad Choulli
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (IX, 81 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
311   $a3-319-33641-X 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aThis book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems.  The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aPartial differential equations
606   $aPhysics
606   $aCancer research
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aCancer Research$3https://scigraph.springernature.com/ontologies/product-market-codes/B11001
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
606   $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006
615  0$aPartial differential equations.
615  0$aPhysics.
615  0$aCancer research.
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615 14$aPartial Differential Equations.
615 24$aMathematical Methods in Physics.
615 24$aCancer Research.
615 24$aApplications of Mathematics.
615 24$aMathematical and Computational Engineering.
676   $a515.26
700   $aChoulli$b Mourad$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472386
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254077903321
996   $aApplications of elliptic Carleman inequalities to Cauchy and inverse problems$91523152
997   $aUNINA