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1、TLFeBOOKPublishedbyImperialCollegePress57SheltonStreetCoventGardenLondonWC2H9HEDistributedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonW
2、C2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.OriginallypublishedinFrenchunderthetitle:‹‹Introductionaucalculdesvariations››©1992Pressespolytechniquesetuniversitairesromandes,Lausanne,Switzerla
3、ndAllrightsreservedINTRODUCTIONTOTHECALCULUSOFVARIATIONSCopyright©2004byImperialCollegePressAllrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandret
4、rievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfr
5、omthepublisher.ISBN1-86094-499-XISBN1-86094-508-2(pbk)PrintedinSingapore.IntroductiontothecalculusofvariationsBernardDacorognaContentsPrefacetotheEnglishEditionixPrefacetotheFrenchEditionxi0Introduction10.1Briefhistoricalcomments......................10.2Mo
6、delproblemandsomeexamples.................30.3Presentationofthecontentofthemonograph...........71Preliminaries111.1Introduction..............................111.2ContinuousandHöldercontinuousfunctions............121.2.1Exercises...........................16
7、1.3Lpspaces...............................161.3.1Exercises...........................231.4Sobolevspaces............................251.4.1Exercises...........................381.5Convexanalysis............................401.5.1Exercises....................
8、.......432Classicalmethods452.1Introduction..............................452.2Euler-Lagrangeequation.......................472.2.1Exercises...........................572.3SecondformoftheEuler-Lagrangee
