reichel w. uniqueness theorems for variational problems by method of transformation groups (springer lnm1841,2004)(isbn 3540218394)(135s)

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1、LectureNotesinMathematics1841Editors:J.--M.Morel,CachanF.Takens,GroningenB.Teissier,Paris3BerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoWolfgangReichelUniquenessTheoremsforVariationalProblemsbytheMethodofTransformationGroups13AuthorWolfgangReichelMathemat

2、ischesInstitutUniversitatBasel¨Rheinsprung21,CH4051Basel,Switzerlande-mail:Wolfgang.Reichel@unibas.chLibraryofCongressControlNumber:2004103794MathematicsSubjectClassification(2000):4902,49K20,35J20,35J25,35J65ISSN0075-8434ISBN3-540-21839-4Springer-VerlagBerlinH

3、eidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindataban

4、ks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.Spr

5、inger-VerlagBerlinHeidelbergNewYorkamemberofBertelsmannSpringerScience+BusinessMediaGmbHhttp://www.springer.de
cSpringer-VerlagBerlinHeidelberg2004PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,eveni

6、ntheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:Camera-readyTEXoutputbytheauthorSPIN:1099783341/3142/du-543210-Printedonacid-freepaperToMirjamPrefaceAclassicalprobleminth

7、ecalculusofvariationsistheinvestigationofcriticalpointsofaC1-functionalL:V→RonanormedspaceV.Typicalexam-
plesareL[u]=L(x,u,∇u)dxwithΩ⊂RnandVaspaceofadmissibleΩfunctionsu:Ω→Rk.Alargevarietyofmethodshasbeeninventedtoob-tainexistenceofcriticalpointsofL.Thepresentw

8、orkaddressesadifferentquestion:UnderwhatconditionsontheLagrangianL,thedomainΩandthesetofadmissiblefunctionsVdoesLhaveatmostonecriticalpoint?Thefollowingsufficientconditionforun