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Phase Space Analysis of Partial Differential Equations

:	Antonio Bove, Ferruccio Colombini, Daniele Del Santo
:	Phase Space Analysis of Partial Differential Equations
:	Birkhäuser Basel
:	9780817645212
:	1
:	CHF 85.10
:

:	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

	Preface	7
	Contents	9
	List of Contributors	11
	Trace theorem on the Heisenberg group on homogeneous hypersurfaces	15
	1 Introduction	15
	2 A Hardy type inequality	20
	3 The proof of the trace and trace lifting theorem	24
	4 Concluding remarks	28
	References	28
	Strong unique continuation and finite jet determination for Cauchy Riemann mappings	30
	1 Introduction	30
	2 Local coordinates	31
	3 Nondegeneracy conditions	33
	4 Necessary conditions and su.cient conditions for finite jet determination	35
	5 Lie group structures and jet parameterization	37
	References	40
	On the Cauchy problem for some hyperbolic operator with double characteristics	42
	1 Introduction and statements	42
	2 The model operator	44
	3 Shibuya solutions	45
	4 Stokes multipliers	47
	5 Asymptotic analysis	49
	6 Final steps in the proof of the necessary condition	55
	References	57
	On the differentiability class of the admissible square roots of regular nonnegative functions	58
	1 Introduction	58
	2 Regularity of well-chosen admissible roots	59
	References	66
	The Benjamin Ono equation in energy space	67
	1 Introduction	67
	2 Bourgain spaces	69
	3 A priori estimate on weak solutions	70
	4 The gauge transformation	71
	5 The existence and uniqueness result	73
	References	74
	Instabilities in Zakharov equations for laser propagation in a plasma	75
	1 Introduction	75
	2 The instability mechanism	78
	3 Scheme of the proof	80
	4 The linear instability	84
	5 The linear equation	89
	6 End of proofs	92
	References	93
	Symplectic strata and analytic hypoellipticity	94
	1 Introduction	94
	2 The symplectic case	95
	3 The example of Baouendi Goulaouic	95
	4 Treves original conjecture	96
	5 The Poisson stratification of S	97
	6 Examples	98
	7 Treves conjecture	98
	8 Symplectic strata of codimension 2	99
	9 Sketch of the proof	100
	References	103
	On the backward uniqueness property for a class of parabolic operators	106
	1 Introduction, statements and remarks	106
	2 Proof of Theorem 1.1	110
	3 Proof of Theorem 1.2	114
	References	116
	Inverse problems for hyperbolic equations	117
	1 Formulation of the problem and the main theorem	117
	2 Hyperbolic systems with Yang Mills potentials and domains with obstacles	120
	3 A geometric optics approach	124
	References	125
	On the optimality of some observability inequalities for plate systems with potentials	127
	1 Introduction	128
	2 Preliminaries	132
	3 The sharp observability estimate	135
	4 Extension of Meshkov s construction to the bi-Laplacian equation	138
	5 Optimality of the observability constant for plate systems	139
	6 Further remarks and open problems	141
	References	141
	Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach	143
	Introduction	143
	1 A general setting and a motivating example	144
	2 Weak symplectic manifolds	149
	3 Right invariant weak Riemannian metrics on Lie groups	157
	4 The Hamiltonian approach	165
	5 Vanishing H0-geodesic distance on groups of diffeomorphisms	171
	6 The regular Lie group of rapidly decreasing diffeomorphisms	179
	7 The diffeomorphism group of S1 or R, and Burgers hierarchy	188
	8 The Virasoro Bott group and the Korteweg de Vries hierarchy	195
	Appendix A Smooth calculus beyond Banach spaces	212
	Appendix B Regular infinite-dimensional Lie groups	216
	References	223
	Non-effectively hyperbolic operators and bicharacteristics	226
	1 Introduction	226
	2 Non-effectively hyperbolic symbols, elementary decomposition and a priori estimates	227
	3 Conditions for elementary decomposition	231
	4 Behavior of bicharacteristics and elementary decomposition	240
	5 Remarks	254
	References	254
	On the Fefferman Phong inequality for systems of PDEs	256
	1 Introduction	256
	2 Background on the Weyl Hörmander calculus	258
	3 A proof by induction on the size of the system	260
	References	274
	Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations	276
	1 Introduction	276
	2 Resonances for time-periodic potentials	278
	3 Strichartz estimates	282
	4 Non-trapping moving obstacles	285
	5 Trapping moving obstacles	289
	References	293
	An elementary proof of Fedili s theorem and extensions	295
	1 Introduction	295
	2 Proof of the theorem	296
	References	298
	Outgoing parametrices and global Strichartz estimates for Schrödinger equations with variable coefficients	299
	1 Introduction	299
	2 Outline of the proofs	305
	References	320
	On the analyticity of solutions of sums of squares of vector fields	322
	1 Global Poisson stratification	324
	2 The analyticity conjectures	328
	References	335