Phase Space Analysis of Partial Differential Equations

Hajer Bahouri, Jean-Yves Chemin (auth.), Antonio Bove, Ferruccio Colombini, Daniele Del Santo (eds.)9780817645113, 0-8176-4511-X

This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory.

Key topics:

* The Cauchy problem for linear and nonlinear hyperbolic equations

* Scattering theory

* Inverse problems

* Hyperbolic systems

* Gevrey regularity of solutions of PDEs

* Analytic hypoellipticity

and unique features:

* Original articles are self-contained with full proofs

* Survey articles give a quick and direct introduction to selected topics evolving at a fast pace

Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.

Table of contents :
Front Matter….Pages i-xiv
Trace theorem on the Heisenberg group on homogeneous hypersurfaces….Pages 1-15
Strong unique continuation and finite jet determination for Cauchy-Riemann mappings….Pages 17-28
On the Cauchy problem for some hyperbolic operator with double characteristics….Pages 29-44
On the differentiability class of the admissible square roots of regular nonnegative functions….Pages 45-53
The Benjamin—Ono equation in energy space….Pages 55-62
Instabilities in Zakharov equations for laser propagation in a plasma….Pages 63-81
Symplectic strata and analytic hypoellipticity….Pages 83-94
On the backward uniqueness property for a class of parabolic operators….Pages 95-105
Inverse problems for hyperbolic equations….Pages 107-116
On the optimality of some observability inequalities for plate systems with potentials….Pages 117-132
Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach….Pages 133-215
Non-effectively hyperbolic operators and bicharacteristics….Pages 217-246
On the Fefferman-Phong inequality for systems of PDEs….Pages 247-266
Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations….Pages 267-285
An elementary proof of Fediĭ’s theorem and extensions….Pages 287-290
Outgoing parametrices and global Strichartz estimates for Schrödinger equations with variable coefficients….Pages 291-313
On the analyticity of solutions of sums of squares of vector fields….Pages 315-329