: Antonio Bove, Ferruccio Colombini, Daniele Del Santo
: Phase Space Analysis of Partial Differential Equations
: Birkhäuser Basel
: 9780817645212
: 1
: CHF 85,70
:
: Analysis
: English
: 329
: Wasserzeichen/DRM
: PC/MAC/eReader/Tablet
: PDF

Covers phase space analysis methods, including microlocal analysis, and their applications to physics

Treats the linear and nonnlinear aspects of the theory of PDEs

Original articles are self-contained with full proofs; survey articles give a quick and direct introduction to selected topics evolving at a fast pace

Excellent reference and resource for grad students and researchers in PDEs and related fields

Preface7
Contents9
List of Contributors11
Trace theorem on the Heisenberg group on homogeneous hypersurfaces15
1 Introduction15
2 A Hardy type inequality20
3 The proof of the trace and trace lifting theorem24
4 Concluding remarks28
References28
Strong unique continuation and finite jet determination for Cauchy Riemann mappings30
1 Introduction30
2 Local coordinates31
3 Nondegeneracy conditions33
4 Necessary conditions and su.cient conditions for finite jet determination35
5 Lie group structures and jet parameterization37
References40
On the Cauchy problem for some hyperbolic operator with double characteristics42
1 Introduction and statements42
2 The model operator44
3 Shibuya solutions45
4 Stokes multipliers47
5 Asymptotic analysis49
6 Final steps in the proof of the necessary condition55
References57
On the differentiability class of the admissible square roots of regular nonnegative functions58
1 Introduction58
2 Regularity of well-chosen admissible roots59
References66
The Benjamin Ono equation in energy space67
1 Introduction67
2 Bourgain spaces69
3 A priori estimate on weak solutions70
4 The gauge transformation71
5 The existence and uniqueness result73
References74
Instabilities in Zakharov equations for laser propagation in a plasma75
1 Introduction75
2 The instability mechanism78
3 Scheme of the proof80
4 The linear instability84
5 The linear equation89
6 End of proofs92
References93
Symplectic strata and analytic hypoellipticity94
1 Introduction94
2 The symplectic case95
3 The example of Baouendi Goulaouic95
4 Treves original conjecture96
5 The Poisson stratification of S97
6 Examples98
7 Treves conjecture98
8 Symplectic strata of codimension 299
9 Sketch of the proof100
References103
On the backward uniqueness property for a class of parabolic operators106
1 Introduction, statements and remarks106
2 Proof of Theorem 1.1110
3 Proof of Theorem 1.2114
References116
Inverse problems for hyperbolic equations117
1 Formulation of the problem and the main theorem117
2 Hyperbolic systems with Yang Mills potentials and domains with obstacles120
3 A geometric optics approach124
References125
On the optimality of some observability inequalities for plate systems with potentials 127
1 Introduction128
2 Preliminaries132
3 The sharp observability estimate135
4 Extension of Meshkov s construction to the bi-Laplacian equation138
5 Optimality of the observability constant for plate systems139
6 Further remarks and open problems141
References141
Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach143
Introduction143
1 A general setting and a motivating example144
2 Weak symplectic manifolds149
3 Right invariant weak Riemannian metrics on Lie groups157
4 The Hamiltonian approach165
5 Vanishing H0-geodesic distance on groups of diffeomorphisms171
6 The regular Lie group of rapidly decreasing diffeomorphisms179
7 The diffeomorphism group of S1 or R, and Burgers hierarchy188
8 The Virasoro Bott group and the Korteweg de Vries hierarchy195
Appendix A Smooth calculus beyond Banach spaces212
Appendix B Regular infinite-dimensional Lie groups216
References223
Non-effectively hyperbolic operators and bicharacteristics226
1 Introduction226
2 Non-effectively hyperbolic symbols, elementary decomposition and a priori estimates227
3 Conditions for elementary decomposition231
4 Behavior of bicharacteristics and elementary decomposition240
5 Remarks254
References254
On the Fefferman Phong inequality for systems of PDEs256
1 Introduction256
2 Background on the Weyl Hörmander calculus258
3 A proof by induction on the size of the system260
References274
Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations276
1 Introduction276
2 Resonances for time-periodic potentials278
3 Strichartz estimates282
4 Non-trapping moving obstacles285
5 Trapping moving obstacles289
References293
An elementary proof of Fedili s theorem and extensions295
1 Introduction295
2 Proof of the theorem296
References298
Outgoing parametrices and global Strichartz estimates for Schrödinger equations with variable coefficients299
1 Introduction299
2 Outline of the proofs305
References320
On the analyticity of solutions of sums of squares of vector fields322
1 Global Poisson stratification324
2 The analyticity conjectures328
References335