二阶椭圆偏微分方程

图书标准信息

• 作者 D.Gilbarg、N.S.Trudinger 著
• 出版社 世界图书出版公司
• 出版时间 2003-04
• 版次 1
• ISBN 9787506259224
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 517页

【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