Date : 2018
Type : Livre / Book
Langue / Language : anglais / English
ISBN : 978-2-85629-882-4
EAN : 9782856298824
Relativité restreinte (physique)
Équations aux dérivées partielles
Équations différentielles hyperboliques
Résumé / Abstract : This book is dedicated to the construction and the control of a parametrix to the homogeneous wave equation ⎕g∅ = 0, where g is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L² bounds on the curvature tensor R of g is a major step of the proof of the bounded L² curvature conjecture proposed by Sergiu Klainerman and solved by Sergiu Klainerman, Igor Rodnianski and the author. On a more general level, this book deals with the control of the eikonal equation on a rough background, and with the derivation of L² bounds for Fourier integral operators on manifolds with rough phases and symbols, and as such is also of independent interest. [4e de couverture]