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TheexistingmathematicalliteratureonSobolevspacesandtheirgeneralizationsisvast,anditwouldbeneithereasynorparticularlydesirabletoincludeeverythingthatwasknownaboutsuchspacesbetweenthecoversofonebook.Anattempthasbeenmadeinthismonographtopresentallthecorematerialinsufficientgeneralitytocovermostapplications,togivethereaderanoverviewofthesubjectthatisdifficulttoobtainbyreadingresearchpapers,andfinally...toprovideareadyreferenceforsomeonerequiringaresultaboutSobolevspacesforuseinsomeapplication.内容简介
ThismonographpresentsanintroductorystudyofofthepropertiesofcertainBa-nachspacesofweaklydifferentiablefunctionsofseveralrealvariablesthatariseinconnectionwithnumerousproblemsinthetheoryofpartialdifferentialequations,approximationtheory,andmanyotherareasofpureandappliedmathematics.ThesespaceshavebecomeassociatedwiththenameofthelateRussianmathe-maticianS.L.Sobolev,althoughtheiroriginspredatehismajorcontributionstotheirdevelopmentinthelate1930s.目录
Preface
LisfofSpacesandNorms
1.PRELIMINARIES
Notation
TopologicalVectorSpaces
NormedSpaces
SpacesofContinuousFunctions
TheLebesgueMeasureinRn
TheLebesgueIntegral
DistributionsandWeakDerivatives
2.THELEBESGUESPACESLp(Ω)
DefinitionandBasicProperties
CompletenessofLp(Ω)
ApproximationbyContinuousFunctions
ConvolutionsandYoungsTheorem
MollifiersandApproximationbySmoothFunctions
PrecompactSetsinLp(Ω)
UniformConvexity
TheNormedDualofLP(Ω)
Mixed-NormLpSpaces
TheMarcinkiewiczInterpolationTheorem
……前言/序言
ThismonographpresentsanintroductorystudyofofthepropertiesofcertainBa-nachspacesofweaklydifferentiablefunctionsofseveralrealvariablesthatariseinconnectionwithnumerousproblemsinthetheoryofpartialdifferentialequations,approximationtheory,andmanyotherareasofpureandappliedmathematics.ThesespaceshavebecomeassociatedwiththenameofthelateRussianmathe-maticianS.L.Sobolev,althoughtheiroriginspredatehismajorcontributionstotheirdevelopmentinthelate1930s.
Evenby1975whenthefirsteditionofthismonographwaspublished,therewasagreatdealofmaterialonthesespacesandtheircloserelatives,thoughmostofitwasavailableonlyinresearchpaperspublishedinawidevarietyofjournals.ThemonographwaswrittentofillaperceivedneedforasinglesourcewheregraduatestudentsandresearchersinawidevarietyofdisciplinescouldlearntheessentialfeaturesofSobolevspacesthattheyneededfortheirparticularapplications.Noattemptwasmadeevenatthattimeforcompletecoverage.ToquotefromthePrefaceofthefirstedition.