Tools for PDE. Pseudodifferential operators, paradifferential operators, and layer potentials

Cover......Page 1
Title: Tools for PDE......Page 3
QA377.T37 2000   515'.353 — dc2l......Page 5
Contents......Page 8
Preface......Page 10
Introduction......Page 12
1. Spaces of continuous functions......Page 14
2. Operator estimates on L^p, h^2 and bmo......Page 28
3. Symbol classes and symbol smoothing......Page 42
4. Operator estimates on Sobolev-like spaces......Page 48
5. Operator estimates on spaces C^(\lambda)......Page 55
6. Products......Page 65
7. Commutator estimates......Page 69
8. Operators with Sobolev coefficients......Page 72
9. Operators with double symbols......Page 74
10. The CRW commutator estimate......Page 86
12. Estimates on a class of Besov spaces......Page 93
13. Operators with coefficients in a function algebra......Page 97
14. Some BKM-type estimates......Page 99
15. Variations on an estimate of Thmanov......Page 103
16. Estimates on Morrey-type spaces......Page 105
Introduction......Page 112
1. A product estimate......Page 116
2. A commutator estimate......Page 117
3. Some handy estimates involving maximal functions......Page 119
4. A composition estimate......Page 121
5. More general composition estimate......Page 123
6. Continuity of u ---> f(u) on H^(1, p)......Page 124
7. Estimates on F(u) —> F(v)......Page 127
8. A pseudodiffereritial operator estimate......Page 129
9. Paradifferential operators on the spaces C^(\lambda)......Page 131
A. Paracomposition......Page 136
B. Alinhac's lemma......Page 143
Introduction......Page 146
1. Interior elliptic regularity......Page 148
2. Some natural first-order operators......Page 159
3. Estimates for the Dirichlet problem......Page 166
4. Layer potentials on C^1' surfaces......Page 170
5. Parametrix estimates and trace asymptotics......Page 184
6. Euler flows on rough planar domains......Page 189
7. Persistence of solutions to semilinear wave equations......Page 194
8. Div-curl estimates......Page 197
9. Harmonic coordinates......Page 205
10. Riemannian manifolds with bounded Ricci tensor......Page 213
11. Propagation of singularities......Page 216
Introduction......Page 228
1. Cauchy kerne!s on Lipschitz curves......Page 229
2. The method of rotations and extensions to higher dimensions......Page 239
3. The variable-coefficient case......Page 241
4. Boundary integral operators......Page 246
5. The Dirichiet problem on Lipschitz domains......Page 252
A. The Koebe-Bieberbach distortion theorem......Page 257
Bibliography......Page 260
List of Symbols......Page 266
Index......Page 268
Back Cover......Page 269