●Introduction
Chapter XVIISecond Order Elliptic Operators
Summary N
17.1 Interior Regularity and Local Existence Theorems
17.2 UniqueContinuation Tbeorems
17.3 The Dirichlet Problem
17.4 The Hadamard Parametrix Construction
17.5 Asymptotic Properties ofEigenvalues and Eigenfunctions
Notes
Chapter XVIIIPseudo—Differential Operators
Summary
18.1TheBasicCalculus
18.2ConormaIDistributions
18.3 TotallyCharacteristic Operators
18.4 Gauss Transforms Revisited
18.5TheWeylCalculus
18.6 Estimates ofPseudo—DifferentialOperators
Notes
Chapter XIXElliptic Operators on a Compact Manifold Without
Boundary
Summary
19.1AbstractFredholmTheory
19.2 Thelndex ofElliptic Operators
19.3 Tbelndex TheoreminRl
19.4 The Lefschetz Formula
19.5 Miscellaneous Remarks on Ellipticity
Notes
Chapter XXBoundary Problems for Elliptic Differential Operators
Summary
20.1 Elliptic Boundary Problems
20.2 Preliminaries on Ordinary Differential Operators
20.3 Thelndex for Elliptic Boundary Problems
20.4 Non—Elliptic Boundary Problems
Notes
Chapter XXI.Symplectic Geometry
Summary
21.1 The Basic Structure
21.2 Submanifolds ofa Sympletic Manifold
21.3 Normal Forms ofFunctions
21.4 Folds and Glancing Hypersurfaces
21.5 Symplectic Equivalence ofQuadratic Forms
21.6 The Lagrangian Grassmannian
Notes '
Chapter XXIISome Classes of（Micro—）hypoelliptic Operators
Summary
22.1 Operators with Pseudo—Differential Parametrix
22.2 Generalized Kolmogorov Equations
22.3Melin'slnequality
22.4 Hypoellipticity with Loss of One Derivative
Notes
Chapter XXIIIThe Strictly hyperbolic Cauchy Problem
Summary
23.1 First OrderOperators
23.2 Operators ofHigher Order
23.3 Necessary Conditions for Correctness of the Cauchy
Problem
23.4 Hyperbolic Operators of PrincipaIType
Notes
Chapter XXIVThe Mixed Dirichlet—Cauchy Problem for Second Order
Operators
Summary
24.1 Energy Estimates and Existence Theorems in the Hyperbolic Case
24.2 Singularities in the Elliptic and Hyperbolic Regions
24.3 The Generalized Bicharacteristic Flow
24.4 The Diffractive Case
24.5 The General Propagation ofSingularities
24.6 Operators Microlocally ofTricomi's Type
24.7 Operators Depending on Parameters
Notes
Appendix BSome Spaces of Distributions
B.1 Distributions in R and in an Open Manifold
B.2 Distributions in a Half Space and in a Manifold with Boundary N
Appendix CSome Tools from Differential Geometry
C.1 The Frobenius Theorem and Foliations
C.2 A Singular Differential Equation
C.3 Clean Intersections and Maps of Constant Rank
C.4 Folds and Involutions
C.5 Geodesic Normal Coordinates
C.6 The Morse Lemma with Parameters
Notes
Bibliography
Index
Index of Notation

本書作者是世界公認的數學分析領頭學者，這套4卷集的經典名著以廣義函數論為框架，論述了與偏微分方程理論有關的經典分析和現代分析的許多精華內容。第3卷目次：二階橢圓算子；偽微分算子；無界緊流形上的橢圓算子；橢圓微微算子的邊界值問題；辛幾何；亞橢圓算子的類別；嚴格雙曲柯西問題；二階算子的混合狄利克雷（Dirichlet）-柯西問題。

(瑞典)L.赫爾曼德爾(Lars Hormander) 著 著