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Degenerate Elliptic Equations Book

Degenerate Elliptic Equations
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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
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  • Degenerate Elliptic Equations
  • Written by author Serge Levendorskii
  • Published by Springer-Verlag New York, LLC, 12/9/2010
  • 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
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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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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

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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

Degenerate Elliptic Equations

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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

Degenerate Elliptic Equations

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