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Introduction | 1 | |
1 | General Calculus of Pseudodifferential Operators | 9 |
1.1 | Weyl-Hormander Calculus | 9 |
1.2 | The Calculus of Pseudodifferential Operators with Double Symbols | 45 |
2 | Model Classes of Degenerate Elliptic Differential Operators | 75 |
2.1 | Classes of Operators and Weighted Sobolev Spaces | 75 |
2.2 | Operators of Type 1 (Strong Degeneration Case) | 81 |
2.3 | Operators of Type 2 (Ellipticity along Boundary and Strong Degeneration in Normal Direction) | 87 |
2.4 | Operators of Type 3 (Ellipticity along Boundary and Euler Operators in Normal Direction) | 95 |
2.5 | Operators of Type 4 (Equations which Require Boundary and Coboundary Conditions) | 98 |
3 | General Classes of Degenerate Elliptic Differential Operators | 129 |
3.1 | Definition of Types of Operators and their Symbols | 129 |
3.2 | Operators of Type 1 | 135 |
3.3 | Operators of Type 4 | 145 |
3.4 | Operators of Types 2, 3 | 158 |
4 | Degenerate Elliptic Operators in Non-Power-Like Degeneration Case | 163 |
4.1 | Operators of Type 1 - 3 | 163 |
4.2 | Operators of Type 4 | 165 |
5 | L[subscript p]-Theory for Degenerate Elliptic Operators | 171 |
5.1 | L[subscript p]-Theory for Pseudodifferential Operators with Double Symbols | 171 |
5.2 | Operators of Type 1 | 180 |
5.3 | Operators of Type 4 | 182 |
6 | Coersiveness of Degenerate Quadratic Forms | 187 |
6.1 | Types of Degenerate Quadratic Forms and their Symbols | 187 |
6.2 | Forms of Type 1 | 190 |
6.3 | Forms of Type 4 | 193 |
6.4 | Forms of Types 2, 3 | 199 |
6.5 | Forms of Type 3 | 202 |
7 | Some Classes of Hypoelliptic Pseudodifferential Operators on Closed Manifold | 203 |
7.1 | Operators of Slowly Varying Order | 203 |
7.2 | Hypoelliptic Operators with Multiple Characteristics | 213 |
7.3 | Weighted Sobolev Spaces and Hypoelliptic Operators with Multiple Characteristics as Fredholm Operators | 225 |
7.4 | Interior Boundary Value Problem | 239 |
8 | Algebra of Boundary Value Problems for Class of Pseudodifferential Operators which Change Order on the Boundary | 245 |
8.1 | Symbols on [actual symbol not reproducible] | 245 |
8.2 | Classes of operators on Half-Space | 251 |
8.3 | Weighted Sobolev Spaces | 262 |
8.4 | Operators on Closed Manifolds with Boundaries | 270 |
8.5 | An Index Theorem | 275 |
9 | General Schemes of Investigation of Spectral Asymptotics for Degenerate Elliptic Equations | 279 |
9.1 | General Theorems on Spectral Asymptotics | 279 |
9.2 | General Schemes of Investigation of Spectral Asymptotics and Generalizations of the Weyl Formula for Degenerate Elliptic Operators | 291 |
10 | Spectral Asymptotics of Degenerate Elliptic Operators | 301 |
10.1 | Formal Computations of Spectral Asymptotics for Operators of All Types | 301 |
10.2 | Proof of the Asymptotic Formulae | 317 |
11 | Spectral Asymptotics of Hypoelliptic Operators with Multiple Characteristics | 335 |
11.1 | Formal Computations of Spectral Asymptotics | 335 |
11.2 | Proofs of the Asymptotic Formulae | 355 |
A Brief Review of the Bibliography | 389 | |
Bibliography | 399 | |
Index of Notation | 423 |
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Add Degenerate Elliptic Equations, This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appro, Degenerate Elliptic Equations to the inventory that you are selling on WonderClubX
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Add Degenerate Elliptic Equations, This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appro, Degenerate Elliptic Equations to your collection on WonderClub |