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1、VBarbuUniversityofIa§iOptimalcontrolofvariationalinequalitiesPitmanAdvancedPublishingProgramBOSTON·LONDON·MELBOURNEPITMANPUBLISHINGLIMITED128LongAcre,LondonWC2E9ANPITMANPUBLISHINGINC1020PlainStreet,Marshfield,Massachusetts02050AssociatedCompaniesPitmanPublishingPtyLtd,MelbournePitman
2、PublishingNewZealandLtd,WellingtonCoppClarkPitman,Toronto©VBarbu1984Firstpublished1984AMSSubjectClassifications:(main)49A29,49B21,49B22(subsidiary)35J65,35J85,35K60LibraryofCongressCataloginginPublicationDataBarbu,Viorel.Optimalcontrolofvariationalinequalities.Bibliography:p.1.Variat
3、ionalinequalities(Mathematics)2.Dif•ferentialequations,Elliptic.3.Differentialequations,Parabolic.I.Title.QA316.B281984515'.6483-25007ISBN0-273-08629-4BritishLibraryCataloguinginPublicationDataBarbu,V.Optimalcontrolofvariationalinequalities.-(Researchnotesinmathematics;100)1.Calculat
4、ionsofvariations2.InequalitiesI.TitleII.Series515'.64QA316ISBN0-273-08629-4Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingand/orotherwise,withoutthepriorwrittenpermissio
5、nofthepublishers.Thisbookmaynotbelent,resold,hiredoutorotherwisedisposedofbywayoftradeinanyformofbindingorcoverotherthanthatinwhichitispublished,withoutthepriorconsentofthepublishers.ReproducedandprintedbyphotolithographyinGreatBritainbyBiddIesLtd,GuildfordPrefaceThisbookisconcernedw
6、iththetheoryoffirst-ordernecessaryconditionsofoptimalityforcontrolproblemsgovernedbyvariationalinequalitiesandsemilinearequationsofellipticandparabolictype.ItisapleasuretoacknowledgetheconsiderableinfluenceoftheworksofProfessorJ.L.Lions,andtheauthortakesthisopportunitytothankhimforhi
7、sinterestinthedevelopmentofthepresentwork.ThanksarealsoduetoDrD.JibaandDrO.Carjaforreadingthemanu•scriptandsuggestinganumberofchanges.Partofthisbookwaswrittenandpartofthepreliminaryresearchin•volvedinitspreparationwascarriedoutwhiletheauthorwasatINRIA,Rocquencourt,in1980andatPurdueUn
8、iversityinFe