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1、PublishedbyImperialCollegePress57SheltonStreetCoventGardenLondonWC2H9HEDistributedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBr
2、itishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.OriginallypublishedinFrenchunderthetitle:‹‹Introductionaucalculdesvariations››©1992Pressespolytechniquesetuniversitairesromandes,Lausanne,SwitzerlandAllrig
3、htsreservedINTRODUCTIONTOTHECALCULUSOFVARIATIONSCopyright©2004byImperialCollegePressAllrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsy
4、stemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepub
5、lisher.ISBN1-86094-499-XISBN1-86094-508-2(pbk)PrintedinSingapore.ContentsPrefacetotheEnglishEditionixPrefacetotheFrenchEditionxi0Introduction10.1Briefhistoricalcomments......................10.2Modelproblemandsomeexamples.................30.3Presentationoft
6、hecontentofthemonograph...........71Preliminaries111.1Introduction..............................111.2ContinuousandHöldercontinuousfunctions............121.2.1Exercises...........................161.3Lpspaces...............................161.3.1Exercises...
7、........................231.4Sobolevspaces............................251.4.1Exercises...........................381.5Convexanalysis............................401.5.1Exercises...........................432Classicalmethods452.1Introduction..................
8、............452.2Euler-Lagrangeequation.......................472.2.1Exercises...........................572.3SecondformoftheEuler-Lagrangeequation............592.3.1Exercises..........................
