偏微分方程（第3卷）

　　Introduction 13 Function Space and Operator Theory for Nonlinear Analysis Introduction 1 Lp-Sobolev spaces 2 Sobolev imbedding theorems 3 Gagliardo-Nirenberg-Moser estimates 4 Tmdinger's inequalities 5 Singular integral operators on Lp 6 The spaces Hs，p 7 Lp-spectral theory of the Laplace operator 8 Holder spaces and Zygmund spaces 9 Pseudodifferential operators with nonregular symbols 10 Paradifferential operators 11 Young measures and fuzzy functions 12 Hardy spaces References.本书为英文版。

暂缺《偏微分方程（第3卷）》作者简介

ContentsofVolumesIandII
Introduction
13FunctionSpaceandOperatorTheoryforNonlinearAnalysis
Introduction
1Lp-Sobolevspaces
2Sobolevimbeddingtheorems
3Gagliardo-Nirenberg-Moserestimates
4Tmdinger'sinequalities
5SingularintegraloperatorsonLp
6ThespacesHs,p
7Lp-spectraltheoryoftheLaplaceoperator
8HolderspacesandZygmundspaces
9Pseudodifferentialoperatorswithnonregularsymbols
10Paradifferentialoperators
11Youngmeasuresandfuzzyfunctions
12Hardyspaces
References
14NonlinearEllipticEquations
Intxoduction
1Aclassofsemilinearequations
2Surfaceswithnegativecurvature
3Localsolvabilityofnonlinearellipticequations
4EllipticregularityI(interiorestimates)
5IsometricimbeddingofRiemannianmanifolds
6Minimalsurfaces
6BSecondvariationofarea
7Theminimalsurfaceequation
8EllipticregularityII(boundaryestimates)
9EllipticregularityIII(DeGiorgi-Nash-Mosertheory)
10TheDirichletproblemforquasi-linearellipticequations
11Directmethodsinthecalculusofvariations
12Quasi-linearellipticsystems
12BFurtherresultsonquasi-linearsystems
13EllipticregularityIV(Krylov-Safonovestimates)
14Regularityforaclassofcompletelynonlinearequations
15Monge-Ampereequations
16Ellipticequationsintwovariables
AMorreyspaces
BLeray-Schauderfixed-pointtheorems
References
15NonlinearParabolicEquations
Introduction
1Semilinearparabolicequations
2AppliCationstoharmonicmaps
3Semilinearequationsonregionswithboundary
4Reaction-diffusionequations
5AnonlinearTrotterproductformula
6TheStefanproblem
7Quasi-linearparabolicequationsI
8Quasi-linearparabolicequationsII(sharperestimates)
9Quasi-linearparabolicequationsIII(Nash-Moserestimates)
References
16NonlinearHyperbolicEquations
Introduction
1Quasi-linear,symmetrichyperbolicsystems
2Symmetrizablehyperbolicsystems
3Second-orderandhigher-orderhyperbolicsystems
4EquationsinthecomplexdomainandtheCauchy-Kowalewsky
theorem
5Compressiblefluidmotion
6Weaksolutionstoscalarconservationlaws;theviscosity
method
7Systemsofconservationlawsinonespacevariable;Riemann
problems
8Entropy-fluxpairsandRiemanninvariants
9Globalweaksolutionsofsome2×2systems
10Vibratingstringsrevisited
References
17EulerandNavier-StokesEquationsforIncompressibleFluids
Introduction
1Euler'sequationsforidealincompressiblefluidflow
2ExistenceofsolutionstotheEulerequations
3Eulerflowsonboundedregions
4Navier-Stokesequations
5Viscousflowsonboundedregions
ARegularityfortheStokessystemonboundeddomains
References
18Einstein'sEquations
Introduction
1Thegravitationalfieldequations
2SphericallysymmetricspacetimesandtheSchwarzschild
solution
3Stationaryandstaticspacetimes
4OrbitsinSchwarzschildspacetime
5CoupledMaxwell-Einsteinequations
6Relativisticfluids
7Gravitationalcollapse
8Theinitial-valueproblem
9Geometryofinitialsurfaces
10Timeslicesandtheirevolution
References
Index