Parametrix for wave equations on a rough background III : space-time regularity of the phase - Szeftel, Jeremie (Paris : Societe Mathematique de France, 2018)
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 L bounds on the curvature tensor R of g is a major step of the proof of the bounded L 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 L bounds for Fourier integral operators on manifolds with rough phases and symbols, and as such is also of independent interest.
Includes bibliographical references and index.
Includes abstract in English and French.
Keywords: Wave equation; Einstein field equations