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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.

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