非线形泛函分析及其应用：线性单调算子（第2A卷）

图书标准信息

• 作者 [德]宰德勒 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005206
• 定价 69.00元
• 装帧 精装
• 开本 24开
• 纸张 胶版纸
• 页数 467页
• 正文语种 英语

【内容简介】

　　自1932年，波兰数学家Banach发表第一部泛函分析专著“Theoriedesoperationslineaires”以来，这一学科取得了巨大的发展，它在其他领域的应用也是相当成功。如今，数学的很多领域没有了泛函分析恐怕寸步难行，不仅仅在数学方面，在理论物理方面的作用也具有同样的意义，M．Reed和B．Simon的“MethodsofModernMathematicalPhysjcs”在前言中指出：“自1926年以来，物理学的前沿已与日俱增集中于量子力学，以及奠定于量子理论的分支：原子物理、核物理固体物理、基本粒子物理等，而这些分支的中心数学框架就是泛函分析。”所以，讲述泛函分析的文献已浩如烟海。而每个时代，都有这个领域的代表性作品。

【目录】

PrefacetoPartII/A
INTRODUCTIONTOTHESUBJECT
CHAPTER18
VariationalProblems，theRitzMethod，and
theIdeaofOrthogonality
18.1.TheSpaceC(G)andtheVariationalLemma
18.2.IntegrationbyParts
18.3.TheFirstBoundaryValueProblemandtheRitzMethod
18.4.TheSecondandThirdBoundaryValueProblemsand
theRitzMethod
18.5.EigenvalueProblemsandtheRitzMethod
18.6.TheH61derInequalityanditsApplications
18.7.TheHistoryoftheDirichletPrincipleandMonotoneOperators
18.8.TheMainTheoremonQuadraticMinimumProblems
18.9.TheInequalityofPoincar6-Friedrichs
18.10.TheFunctionalAnalyticJustificationoftheDirichletPrinciple
18.11.ThePerpendicularPrinciple，theRieszTheorem，and
theMainTheoremonLinearMonotoneOperators
18.12.TheExtensionPrincipleandtheCompletionPrinciple
18.13.ProperSubregions
18.14.TheSmoothingPrinciple
18.15.TheIdeaoftheRegularityofGeneralizedSolutionsand
theLemmaofWeyl
18.16.TheLocalizationPrinciple
18.17.ConvexVariationalProblems，EllipticDifferentialEquations，
andMonotonicity
18.18.TheGeneralEuler-LagrangeEquations
18.19.TheHistoricalDevelopmentofthe19thand20thProblemsof
HilbertandMonotoneOperators
18.20.SufficientConditionsforLocalandGlobalMinimaand
LocallyMonotoneOperators

CHAPTER19
TheGalerkinMethodforDifferentialandIntegralEquations，
theFriedrichsExtension，andtheIdeaofSelf-Adjointness
19.1.EllipticDifferentialEquationsandtheGalerkinMethod
19.2.ParabolicDifferentialEquationsandtheGalerkinMethod
19.3.HyperbolicDifferentialEquationsandtheGalerkinMethod
19.4.IntegralEquationsandtheGalerkinMethod
!9.5.CompleteOrthonormalSystemsandAbstractFourierSeries
19.6.EigenvaluesofCompactSymmetricOperators
(Hilbert-SchmidtTheory)
19.7.ProofofTheorem19.B
19.8.Self-AdjointOperators
19.9.TheFriedrichsExtensionofSymmetricOperators
19.10.ProofofTheorem19.C
19.11.ApplicationtothePoissonEquation
19.12.ApplicationtotheEigenvalueProblemfortheLaplaceEquation
19.13.TheInequalityofPoincar6andtheCompactness
TheoremofRellich
19.14.FunctionsofSelf-AdjointOperators
19.15.ApplicationtotheHeatEquation
19.16.ApplicationtotheWaveEquation
19.17.SemigroupsandPropagators，andTheirPhysicalRelevance
19.18.MainTheoremonAbstractLinearParabolicEquations
!9.19.ProofofTheorem19.D
!9.20.MonotoneOperatorsandtheMainTheoremon
LinearNonexpansiveSemigroups
19.21.TheMainTheoremonOne-ParameterUnitaryGroups
19.22.ProofofTheorem19.E
19.23.AbstractSemilinearHyperbolicEquations
19.24.ApplicationtoSemilinearWaveEquations
19.25.TheSemilinearSchr6dingerEquation
19.26.AbstractSemilinearParabolicEquations，FractionalPowersof
Operators，andAbstractSobolevSpaces
19.27.ApplicationtoSemilinearParabolicEquations
19.28.ProofofTheorem19.1
19.29.FiveGeneralUniquenessPrinciplesandMonotoneOperators
19.30.AGeneralExistencePrincipleandLinearMonotoneOperators

CHAPTER20
DifferenceMethodsandStability
20.1.Consistency，Stability，andConvergence
20.2.ApproximationofDifferentialQuotients
20.3.ApplicationtoBoundaryValueProblemsfor
OrdinaryDifferentialEquations
20.4.ApplicationtoParabolicDifferentialEquations
20.5.ApplicationtoEllipticDifferentialEquations
20.6.TheEquivalenceBetweenStabilityandConvergence
20.7.TheEquivalenceTheoremofLaxforEvolutionEquations
LINEARMONOTONEPROBLEMS

CHAPTER21
AuxiliaryToolsandtheConvergenceoftheGalerkin
MethodforLinearOperatorEquations
21.1.GeneralizedDerivatives
21.2.SobolevSpaces
21.3.TheSobolevEmbeddingTheorems
21.4.ProofoftheSobolevEmbeddingTheorems
21.5.DualityinB-Spaces
21.6.DualityinH-Spaces
21.7.TheIdeaofWeakConvergence
21.8.TheIdeaofWeak*Convergence
21.9.LinearOperators
21.10.BilinearForms
21.11.ApplicationtoEmbeddings
21.12.ProjectionOperators
21.13.BasesandGalerkinSchemes
21.14.ApplicationtoFiniteElements
21.15.Riesz-SchauderTheoryandAbstractFredholmAlternatives
21.16.TheMainTheoremontheApproximation-SolvabilityofLinear
OperatorEquations，andtheConvergenceoftheGalerkinMethod
21.17.InterpolationInequalitiesandaConvergenceTrick
21.18.ApplicationtotheRefinedBanachFixed-PointTheoremand
theConvergenceofIterationMethods
21.19.TheGagliardo-NirenbergInequalities
21.20.TheStrategyoftheFourierTransformforSobolevSpaces
21.21.BanachAlgebrasandSobolevSpaces
21.22.Moser-TypeCalculusInequalities
21.23.WeaklySequentiallyContinuousNonlinearOperatorson
SobolevSpaces

CHAPTER22
HilbertSpaceMethodsandLinearEllipticDifferentialEquations
22.1.MainTheoremonQuadraticMinimumProblemsandthe
RitzMethod
22.2.ApplicationtoBoundaryValueProblems
22.3.TheMethodofOrthogonalProjection，Duality，andaposteriori
ErrorEstimatesfortheRitzMethod
22.4.ApplicationtoBoundaryValueProblems
22.5.MainTheoremonLinearStronglyMonotoneOperatorsand
theGalerkinMethod
22.6.ApplicationtoBoundaryValueProblems
22.7.CompactPerturbationsofStronglyMonotoneOperators，
FredholmAlternatives，andtheGalerkinMethod
22.8.ApplicationtoIntegralEquations
22.9.ApplicationtoBilinearForms
22.10.ApplicationtoBoundaryValueProblems
22.11.EigenvalueProblemsandtheRitzMethod
22.12.ApplicationtoBilinearForms
22.13.ApplicationtoBoundary-EigenvalueProblems
22.14.GarrdingForms
22.15.TheGardingInequalityforEllipticEquations
22.16.TheMainTheoremsonGardingForms
22.17.ApplicationtoStronglyEllipticDifferentialEquationsofOrder2m
22.18.DifferenceApproximations
22.19.InteriorRegularityofGeneralizedSolutions
22.20.ProofofTheorem22.H
22.21.RegularityofGeneralizedSolutionsuptotheBoundary
22.22.ProofofTheorem22.I

CHAPTER23
HilbertSpaceMethodsandLinearParabolicDifferentialEquations
23.1.ParticularitiesintheTreatmentofParabolicEquations
23.2.TheLebesgueSpaceLp(0，T;X)ofVector-ValuedFunctions
23.3.TheDualSpacetoLp(O，T;X)
23.4.EvolutionTriples
23.5.GeneralizedDerivatives
23.6.TheSobolevSpaceWp(0，T;V，H)
23.7.MainTheoremonFirst-OrderLinearEvolutionEquationsand
theGalerkinMethod
23.8.ApplicationtoParabolicDifferentialEquations
23.9.ProofoftheMainTheorem

CHAPTER24
HilbertSpaceMethodsandLinearHyperbolic
DifferentialEquations
24.1.MainTheoremonSecond-OrderLinearEvolutionEquations
andtheGalerkinMethod
24.2.ApplicationtoHyperbolicDifferentialEquations
24.3.ProofoftheMainTheorem