Parametrix for wave equations on a rough background. IV, Control of the error term / Jérémie Szeftel.

Format:

Book

Author/Creator:

Szeftel, Jérémie, 1977- author.

Contributor:

Société mathématique de France, issuing body.

Series:

Astérisque ; 0303-1179 444.

Astérisque, 0303-1179 ; Numéro 444

Language:

English

French

Subjects (All):

Wave equation.

Einstein field equations.

Differential equations, Partial.

Fourier integral operators.

Physical Description:

viii, 314 pages : illustrations ; 24 cm.

Other Title:

Control of the error term

Place of Publication:

Paris : Société Mathématique de France, 2023.

Language Note:

Text in English, abstract also in French.

Summary:

This book is dedicated to the construction and the control of a parametrix to the homogeneous wave equation []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 Klainerman (2000), and solved jointly in Klainerman, Rodnianski & Szeftel (2015). 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. -- Back cover.

Notes:

"Astérisque est un périodique de la Société Mathématique de France. Numéro 444, 2023"--Cover page 2.

"Texte soumis en avril 2012 et accepté en avril 2023"--Verso of title page.

Includes bibliographical references (pages 313-314).

ISBN:

9782856299784

2856299784

OCLC:

1414009377