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二阶椭圆偏微分方程

二阶椭圆偏微分方程
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作者: 著 , 著
出版社: 世界图书出版公司
2003-04
版次: 1
ISBN: 9787506259224
定价: 59.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 517页
分类: 自然科学
117人买过
  • Thisrevisionofthe1983secondeditionof"EllipticPartialDifferentialEquationsofSecondOrder"correspondstotheRussianedition，publishedin1989，inwhichweessentiallyupdatedthepreviousversionto1984.TheadditionaltextrelatestotheboundaryH61derderivativeestimatesofNikolaiKrylov，whichprovidedafundamentalcomponentofthefurtherdevelopmentoftheclassicaltheoryofelliptic(andparabolic)，fullynonlinearequationsinhigherdimensions.InourpresentationweadaptedasimplificationofKrylovsapproachduetoLuisCaffarelli. Chapter1.Introduction
    PartⅠLinearEquations
    Chapter2Laplace’sEquation
    2.1TheMeanValueInequalities
    2.2MaximumandMinimumPrinciple
    2.3TheHarnackInequality
    2.4Green’sRepresentation
    2.5ThePoissonIntegral
    2.6ConvergenceTheorems
    2.7InteriorEstimatesofDerivatives
    2.8TheDirichletProblem；theMethodofSubharmonicFunctions
    2.9Capacity
    Problems
    Chapter3TheClassicalMaximumPrinciple
    3.1TheWeakMaximumPrinciple
    3.2TheStrongMaximumPrinciple
    3.3AprioriBounds
    3.4GradientEstimatesforPoisson’sEquation
    3.5AHarnackInequality
    3.6OperatorsinDivergenceForm
    Notes
    Problems
    Chapter4PoissonsEquationandtheNewtonianPotential
    4.1HolderContinuity
    4.2TheDirichletProblemforPoissonsEquation
    4.3HolderEstimatesfortheSecondDerivatives
    4.4EximatesattheBoundary
    4.5HolderEstimatesfortheFirstDerivatives
    Notes
    Problems
    Chapter5BanachandHilbertSpaces
    5.1TheContractionMappingPrinciple
    5.2TheMethodofContinity
    5.3TheFredholmAlternative
    5.4DualSpacesandAdjoints
    5.5HilbertSpaces
    5.6TheProjectionTheorem
    5.7TheRieszRepresenationTheorem
    5.8TheLax-MilgramTheorem
    5.9TheFredholmAlternativeinHilbertSpaces
    5.10WeakCompactness
    Notes
    Problems
    Chapter6CalssicalSolutions;theSchauderApproach
    Chapter7SobolevSpaces
    Chapter8GeneralizedSolutionaandregularity
    Chapter9StrongSolutions
    PartⅡQuasilinearEquations
    Chapter10MaximumandComparisonPrinciples
    Chapter11TopologicalFixedPointTheoremsandTheirApplication
    Chapter12EquationinTwoVarables
    Chapter13HolderExtimatesfortheCradient
    Chapter14BoundaryGradientEstimates
    Chapter15GlobalandInteriorGradientBounds
    Chapter16EquationsofMeanCurvatureType
    Chapter17FullyNonlinearEquations
    Bibliography
    Epilogue
    SubjectIndex
    NotationIndex
  • 内容简介:
    Thisrevisionofthe1983secondeditionof"EllipticPartialDifferentialEquationsofSecondOrder"correspondstotheRussianedition，publishedin1989，inwhichweessentiallyupdatedthepreviousversionto1984.TheadditionaltextrelatestotheboundaryH61derderivativeestimatesofNikolaiKrylov，whichprovidedafundamentalcomponentofthefurtherdevelopmentoftheclassicaltheoryofelliptic(andparabolic)，fullynonlinearequationsinhigherdimensions.InourpresentationweadaptedasimplificationofKrylovsapproachduetoLuisCaffarelli.
  • 目录:
    Chapter1.Introduction
    PartⅠLinearEquations
    Chapter2Laplace’sEquation
    2.1TheMeanValueInequalities
    2.2MaximumandMinimumPrinciple
    2.3TheHarnackInequality
    2.4Green’sRepresentation
    2.5ThePoissonIntegral
    2.6ConvergenceTheorems
    2.7InteriorEstimatesofDerivatives
    2.8TheDirichletProblem；theMethodofSubharmonicFunctions
    2.9Capacity
    Problems
    Chapter3TheClassicalMaximumPrinciple
    3.1TheWeakMaximumPrinciple
    3.2TheStrongMaximumPrinciple
    3.3AprioriBounds
    3.4GradientEstimatesforPoisson’sEquation
    3.5AHarnackInequality
    3.6OperatorsinDivergenceForm
    Notes
    Problems
    Chapter4PoissonsEquationandtheNewtonianPotential
    4.1HolderContinuity
    4.2TheDirichletProblemforPoissonsEquation
    4.3HolderEstimatesfortheSecondDerivatives
    4.4EximatesattheBoundary
    4.5HolderEstimatesfortheFirstDerivatives
    Notes
    Problems
    Chapter5BanachandHilbertSpaces
    5.1TheContractionMappingPrinciple
    5.2TheMethodofContinity
    5.3TheFredholmAlternative
    5.4DualSpacesandAdjoints
    5.5HilbertSpaces
    5.6TheProjectionTheorem
    5.7TheRieszRepresenationTheorem
    5.8TheLax-MilgramTheorem
    5.9TheFredholmAlternativeinHilbertSpaces
    5.10WeakCompactness
    Notes
    Problems
    Chapter6CalssicalSolutions;theSchauderApproach
    Chapter7SobolevSpaces
    Chapter8GeneralizedSolutionaandregularity
    Chapter9StrongSolutions
    PartⅡQuasilinearEquations
    Chapter10MaximumandComparisonPrinciples
    Chapter11TopologicalFixedPointTheoremsandTheirApplication
    Chapter12EquationinTwoVarables
    Chapter13HolderExtimatesfortheCradient
    Chapter14BoundaryGradientEstimates
    Chapter15GlobalandInteriorGradientBounds
    Chapter16EquationsofMeanCurvatureType
    Chapter17FullyNonlinearEquations
    Bibliography
    Epilogue
    SubjectIndex
    NotationIndex
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