(Ferreira)Carleman estimates and applications to Inverse Problems and Unique Continuation

(Ferreira)Carleman estimates and applications to Inverse Problems and Unique Continuation

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时间:2019-08-03

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1、UNIVERSITÉPARIS13MémoireprésentéparDavidDosSantosFerreiraenvued’obtenirl’HabilitationàdirigerdesrecherchesCarlemanestimatesandapplicationstoInverseProblemsandUniqueContinuationRapporteurs:Prof.NicolasBurq(UniversitéParis11-Orsay)(rapportdeprésentation)Prof.AllanGr

2、eenleaf(RochesterUniversity)Prof.GillesLebeau(UniversitédeNice-SophiaAntipolis)Soutenancele21novembre2011devantlejurycomposéde:Prof.NicolasBurq(UniversitéParis11-Orsay)Prof.Jean-MarcDelort(UniversitéParis13)Prof.AlainGrigis(UniversitéParis13)Prof.GillesLebeau(Univ

3、ersitédeNice-SophiaAntipolis)Prof.LucRobbiano(UniversitédeVersailles-SaintQuentin)Prof.MaciejZworski(UniversityofCalifornia,Berkeley)ContentsIntroduction5Bibliography17Chapter1.Carlemanweights19Introduction191.Geometricpreliminaries192.Euclideancomplexgeometricalo

4、ptics213.Quasimodeconstruction274.LimitingCarlemanweights33Chapter2.Carlemanestimates39Introduction391.L2Carlemanestimateswithdegenerateweights402.LpestimateswithlimitingCarlemanweights433.Relationwithresolventestimates454.ResolventEstimates495.Lpestimateswithpseu

5、doconvexweights596.Uniquecontinuation65Chapter3.Anisotropicinverseproblems69Introduction691.Admissiblegeometries692.Complexgeometricalopticsandidentifiability723.Someanalogies754.Determininganunboundedpotential795.Stabilityestimatesforevolutionequations83Chapter4.I

6、nverseproblemswithpartialdata87Introduction871.Preliminariesandmainresults872.TheWatermelonapproach903.ThemagneticSchrödingeroperator944.Thelinearizedproblem97Chapter5.BoundednessofFourierIntegralOperators103Introduction1031.Preliminariesanddefinitions1032.Nonsmoot

7、hamplitudesandphases1083.Weightedestimates1144.Applications12112CONTENTSAppendices1271.Integraloperatorswithoscillatorykernels1272.SymplecticaspectsoftheL2boundedness1293.Boundarydetermination1324.Theattenuatedgeodesicraytransform135Bibliography141CONTENTS3Remerci

8、ementsJetiensd’abordàremercierNicolasBurqquim’afaitl’amitiédeprésen-tercemémoired’habilitationàlacommissiondeshabilitationsdesuniversitésparisiennes,etd

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