TY  - BOOK
AU  - Szeftel,Jeremie
TI  - Parametrix for wave equations on a rough background III: space-time regularity of the phase 
T2  - Asterisque,
SN  - 9782856298824
U1  - 510=4 23
PY  - 2018///
CY  - Paris :  
PB  - Societe Mathematique de France, 
KW  - Wave equation
KW  - Einstein field equations
N1  - Includes bibliographical references and index
N2  - This book is the third of a sequence of four papers dedicated to the construction and the control of a parametrix to the homogenous wave equation [square]gø=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 in 2000 and solved in 2015 by S. Klainerman, I. 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
ER  -