Applied Nonlinear Functional Analysis: an Introduction PDF
Preview Applied Nonlinear Functional Analysis: an Introduction
NikolaosS.PapageorgiouandPatrickWinkert AppliedNonlinearFunctionalAnalysis Unauthenticated Download Date | 8/12/19 6:46 PM Also of Interest FunctionalAnalysis.ATerseIntroduction GerardoChacón,HumbertoRafeiro,JuanCamiloVallejo,2016 ISBN978-3-11-044191-8,e-ISBN(PDF)978-3-11-044192-5, e-ISBN(EPUB)978-3-11-043364-7 ConvexandSet-ValuedAnalysis.SelectedTopics AramV.Arutyunov,ValeriObukhovskii,2016 ISBN978-3-11-046028-5,e-ISBN(PDF)978-3-11-046030-8, e-ISBN(EPUB)978-3-11-046041-4 ComplexAnalysis.AFunctionalAnalyticApproach FriedrichHaslinger,2017 ISBN978-3-11-041723-4,e-ISBN(PDF)978-3-11-041724-1, e-ISBN(EPUB)978-3-11-042615-1 SingularSolutionsofNonlinearEllipticandParabolicEquations AlexanderA.Kovalevsky,IgorI.Skrypnik,AndreyE.Shishkov,2016 ISBN978-3-11-031548-6,e-ISBN(PDF)978-3-11-033224-7, e-ISBN(EPUB)978-3-11-039008-7 Thed-barNeumannProblemandSchrödingerOperators FriedrichHaslinger,2014 ISBN978-3-11-031530-1,e-ISBN(PDF)978-3-11-031535-6, e-ISBN(EPUB)978-3-11-037783-5 Unauthenticated Download Date | 8/12/19 6:46 PM Nikolaos S.Papageorgiou and Patrick Winkert Applied Nonlinear Functional Analysis | An Introduction Unauthenticated Download Date | 8/12/19 6:46 PM MathematicsSubjectClassification2010 26-XX,28-XX,46-XX,47-XX,49-XX Authors Prof.Dr.NikolaosS.Papageorgiou NationalTechnicalUniversityofAthens DepartmentofMathematics ZografouCampus 15780Athens Greece [email protected] Dr.PatrickWinkert TechnischeUniversitätBerlin InstitutfürMathematik Straßedes17.Juni136 10623Berlin Germany [email protected] ISBN978-3-11-051622-7 e-ISBN(PDF)978-3-11-053298-2 e-ISBN(EPUB)978-3-11-053183-1 LibraryofCongressControlNumber:2018939852 BibliographicinformationpublishedbytheDeutscheNationalbibliothek TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie; detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de. ©2018WalterdeGruyterGmbH,Berlin/Boston Coverimage:NikolaosS.Papageorgiou,PatrickWinkert Typesetting:le-texpublishingservicesGmbH,Leipzig Printingandbinding:CPIbooksGmbH,Leck www.degruyter.com Unauthenticated Download Date | 8/12/19 6:46 PM | Thisbookisdedicatedinmemoryofthefirstauthor’smother M.S.Papageorgiou andinmemoryofthesecondauthor’sfather WolfgangWinkert whobothpassedawayduringitspreparation. Unauthenticated Download Date | 8/12/19 6:46 PM Unauthenticated Download Date | 8/12/19 6:46 PM Preface TheaimofthisbookistopresentthefoundationsofmodernNonlinearFunctional Analysisandequipthereaderwithallthenecessarytoolstocontinuewiththeoretical and/orappliedresearchinthefield.NonlinearFunctionalAnalysisisaverybroad subjectandhasapplicationsinmanydifferentareasofphysics,mechanics,engineering, andeconomics.Infact,itemergedasadistinctdisciplinewithinmathematicalanalysis specificallyasawaytoaddresstheseneedsinamathematicallyrigorousway.Thisway NonlinearFunctionalAnalysisdistinguisheditselffromtheclassicalLinearFunctional Analysisandacquiredaninterdisciplinarycharacter. Thepresentbookprovidesastartingpointtofollowsomeofthemainpathsof NonlinearFunctionalAnalysis,especiallythoseleadingtoapplications.Thegoalis topresentthetheoriesandtechniquestothenewcomer,whichwillallowhim/herto proceedtomorespecializedtopics.Thefirstthreechapterspresentthemainelements oftopology,measuretheory,andBanachspacetheory,whichareneededtoproceed further.Inthelastthreechapterswepresentmoreadvancedandspecializedtopicsthat aremotivatedbytheapplications.InChapter4weexaminecertainspacesoffunctions andmeasuresthatprovidethefunctionalframeworkintheappliedproblems.Wedeal withLebesgue,Lebesgue-Bochner,andSobolevspaces,whicharethebasictoolsinthe studyofboundaryvaluedproblems.Wealsostudyspacesofabsolutelycontinuous functions,offunctionsofboundedvariation,andofmeasuresthateventuallyleadto Youngmeasures.Alltheseconstitutethemoderntoolsindealingwithproblemsof thecalculusofvariations,controltheoryandoptimization,aswellasmathematical economics.InChapter5wedealwithnonsmoothandmultivaluedanalysis,twofieldsof mathematicalanalysisthatemergedsimultaneouslyintheearly1960’sanddeveloped inparallel,feedingeachotherwithnewnotionsandmethods.Asaresult,wedealwith convexfunctionsandtheirdualityandsubdifferentialtheory.Wealsoexaminethe approximationpropertiesofsetsandextendthesubdifferentialtheorytothenonconvex oneintermsoflocallyLipschitzfunctionsinthesenseofClarke.Furthermore,we presentthemaintopologicalandmeasuretheoreticaspectsofset-valuedmapswith applications to integral functionals. In Chapter 6 we finally study topics that are traditionallyassociatedwithwhatiscalled“NonlinearAnalysis.”Theseareoperators ofmonotonetype,degreetheory,fixedpointtheory,variationalprinciplessuchas Ekeland’sVariationalPrinciple,andvariationalconvergencesuchasΓ-orepigraphical convergence.Withthischoiceofmaterial,webelievethatthereaderwillbeproperly equippedattheendtodoresearchinthisexcitingfieldofmathematicalanalysis.Each chapterisfollowedbyatleast50problems.Weencouragethereadertotrythemin ordertotesthis/herunderstandingofthematerial.Thesolutionstotheproblemswill bepostedonthepersonalsiteofthesecondauthor.Ourhopeisthatthereader,with thehelpofthematerialinthisbook,canproceedwithconfidenceinthemanydifferent partsofthisfield. https://doi.org/10.1515/9783110532982-201 Brought to you by | University of Groningen Authenticated Download Date | 8/9/18 12:05 AM VIII | Preface FinallytheauthorswishtothankDr.ApostolosDamialis,MariaDassing,andNadja SchedensackofDeGruyterfortheirkindsupportandhelpduringthepreparationof thisbook. NikolaosS.Papageorgiou,Athens,Greece PatrickWinkert,Berlin,Germany January2018 Brought to you by | University of Groningen Authenticated Download Date | 8/9/18 12:05 AM
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