F.B.I. Transformation: Second Microlocalization and Semilinear Caustics: 1522 (Lecture Notes in Mathematics, 1522) - Softcover

Delort, Jean-Marc

Softcover

ISBN 10: 3540557644 ISBN 13: 9783540557647

Publisher: Springer, 1992

Synopsis

This text grew up from lecturcs givcn at he t University of Rennes I during the academic year 1988-1989. The main topics covered arc second microlocalization along a agrangian l manifold, defined by Sjostrand in [Sj], and its application to the study of conormal sin- gularities for solutions of semilinear hyperbolic partial differential equations, developed by Lebeau [L4]. To give a quite self-contained treatment of these questions, we induded some de- velopments about FBI transformations and subanalytic geometry. The text is made oi four chapters. In he t first one, we define the Fourier-Bros-Ingolnitzer transionnation and study its main properties. The second chapter deals with second microlocalization along a lagrangian submanifold, and with upper bounds for the wave front set of traces one may obtain using it. The third chapter is devoted to formulas giving geometric upper bounds for the analytic wave front set and for the ser,ond mic:rosllpport of boundary values of ramified functions. Lastly, the fourth chapter applies the preceding methods to the derivation of theorems about the location of microlocal singularities of solutions of scmilinear wave equations with conormw data, in general geometrical situation. Every chapter begins with a short abstract of its contents, where are collected the bibliograph- ical references. Let me now thank all those who made this writing possible. First of all, Gilles Lebeau, from whom I learnt mcrol i ocal analysis, especially through lectures he gave with Yves Laurent at Ecole Normale Superieure in 1982-1983.

About this title

Synopsis

During the last ten years, FBI transformation and second microlocalization have been used by several authors to solve different problems in the theory of linear or nonlinear partial differential equations. The aim of this book is to give an introduction to these topics, in the spirit of the work of Sjostrand, and to present their recent application to the propagation of conormal singularities for solutions of seminlinear hyperbolic equations, due to Lebeau. The text is quite self-contained and provides a useful entry to the subject and a bridging link to more specialized papers.

Edition details

• Publisher: Springer
• Publication date: 1992
• Language: English
• ISBN 10: 3540557644
• ISBN 13: 9783540557647
• Binding: Paperback
• Number of pages: 108