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Tables of Contents for Geometric Wave Equations
Chapter/Section Title
Page #
Page Count
Preface
xi
The Wave Equation
1
6
Basic Notations and Concepts from Geometry
1
2
Semilinear Problems
3
1
Wave Maps
3
4
Conservation Laws
7
12
Variational Formulation
7
3
Noether's Theorem
10
3
Method of Multipliers
13
2
Geometric Invariance
15
4
Function Spaces
19
18
Lebesgue and Sobolev Spaces
19
7
Besov Spaces
26
2
Interpolation Theory
28
3
H1 and BMO
31
6
The Linear Wave Equation
37
18
Representation Formulas and Duhamel's Principle
37
7
Fourier Transform Representation
44
1
Pointwise Estimates
45
3
Strichartz-Type Estimates
48
7
Well-Posedness
55
8
Well-Posedness and Local Existence
55
3
Dimensional Analysis and Critical Equations
58
1
Effects of Lorentz Transformation
59
4
Semilinear Wave Equations
63
18
Lipschitz Nonlinearities
63
2
Segal's Theorem
65
4
Jorgens' Theorem
69
3
Critical Growth
72
9
Wave Maps
81
28
Basic Questions
81
1
Geometric Structure
82
7
Analytic Structure
89
2
Algebraic Structure
91
11
Singularities and Nonuniqueness
102
7
Wave Maps with Symmetry
109
20
Equivariant Maps
109
9
The Radial Wave Equation on R2+1
118
5
Regularity of Radial Wave Maps in 2 +1 Dimensions
123
6
Notes
129
6
Bibliography
135