偏微分方程（第2卷）

ContentsofVolumesIandHI
Introduction
7PseudodifferentialOperators
Introduction
1TheFourierintegralrepresentationandsymbolclasses
2Schwartzkernelsofpseudodifferentialoperators
3Adjointsandproducts
4Ellipticoperatorsandparametrices
5LC-estimates
6Garding'sinequality
7Hyperbolicevolutionequations
8Egorov'stheorem
9Microlocalregularity
10Operatorsonmanifolds
11Themethodoflayerpotentials
12Parametrixforregularellipticboundaryproblems
13Parametrixfortheheatequation
14TheWeylcalculus
References
SpectralTheory
Introduction
1Thespectraltheorem
2Self-adjointdifferentialoperators
3Heatasymptoticsandeigenvalueasymptotics
4TheLaplaceoperatoronSn
5TheLaplaceoperatoronhyperbolicspace
6Theharmonicoscillator
7ThequantumCoulombproblem
8TheLaplaceoperatoroncones
References
ScatteringbyObstacles
Introduction
1Thescatteringproblem
2Eigenfunctionexpansions
3Thescatteringoperator
4Connectionswiththewaveequation
5Waveoperators
6TranslationrepresentationsandtheLax-Phillipssemigroup
Z.(t)
7Integralequationsandscatteringpoles
8Traceformulas;thescatteringphase
9Scatteringbyasphere
I0InverseproblemsI
11InverseproblemsII
12Scatteringbyroughobstacles
ALiclskii'stracetheorem
References
10DiracOperatorsandIndexTheory
Introduction
1OperatorsofDiractype
2Cliffordalgebras
3Spinors
4Weitzenbockformulas
5IndexofDh-acoperators
6Proofofthelocalindexformula
7TheChem-Ganss-Bonnettheorem
gSpincmanifolds
9TheRiemann-Rochtheorem
10Directattackin2-D
References
11BrownianMotionandPotentialTheory
Introduction
1BrownianmotionandWienermeasure
2TheFeynman-Kacformula
3TheDirichletproblemanddiffusionondomainswith
boundary
4Martingales,stoppingtimes,andthestrongMarkovproperty
5FirstexittimeandthePoissonintegral~
6Newtoniancapacity
7Stochasticintegrals
8Stochasticintegrals,II
9Stochasticdifferentialequations
10Applicationtoequationsofdiffusion
ATheTrotterproductformula
References
12The9-NeumannProblem
Introduction
AEllipticcomplexes
1Thes-complex
2Morrey'sinequality,theLeviform,andstrongpseudoconvexity
3The-estimateandsomeconsequences
4Higher-ordersubellipticestimates
5Regularityviaellipticregularization
6TheHodgedecompositionandthea-equation
7TheBergmanprojectionandToeplitzoperators
8The-Neumannproblemon(0,q)-forms
9Reductiontopseudodifferentialequationsontheboundary
10The9-equationoncomplexmanifoldsandalmostcomplex
manifolds
BComplementsontheLeviform
CTheNeumannoperatorfortheDirichletproblem
References
CConnectionsandCurvature
Introduction
1Covariantderivativesandcurvatureongeneralvectorbundles
2Secondcovariantderivativesandcovariant-exteriorderivatives
3ThecurvaturetensorofaRiemnnnianmanifold
4Geometryofsubmanifoldsandsubbondles
5TheGauss-Bonnettheoremforsurfaces
6Theprincipalbundlepicture
7TheChern-Weilconstruction
8TheCbern-Gauss-Bonnettheorem
References
Index