| Softcover ISBN: | 978-2-85629-882-4 |
| Product Code: | AST/401 |
| List Price: | $90.00 |
| AMS Member Price: | $72.00 |
| Softcover ISBN: | 978-2-85629-882-4 |
| Product Code: | AST/401 |
| List Price: | $90.00 |
| AMS Member Price: | $72.00 |
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Book DetailsAstérisqueVolume: 401; 2018; 321 ppMSC: Primary 83; Secondary 35; 58
This book is dedicated to the construction and the control of a parametrix to the homogeneous wave equation \(\square_{\mathbf{g}}\phi=0\), where \(\mathbf{g}\) is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes \(L^2\) bounds on the curvature tensor \(\mathbf{R}\) of \(\mathbf{g}\) is a major step of the proof of the bounded \(L^2\) 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 \(L^2\) bounds for Fourier integral operators on manifolds with rough phases and symbols, and as such is also of independent interest.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians interested in wave equations.
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This book is dedicated to the construction and the control of a parametrix to the homogeneous wave equation \(\square_{\mathbf{g}}\phi=0\), where \(\mathbf{g}\) is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes \(L^2\) bounds on the curvature tensor \(\mathbf{R}\) of \(\mathbf{g}\) is a major step of the proof of the bounded \(L^2\) 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 \(L^2\) bounds for Fourier integral operators on manifolds with rough phases and symbols, and as such is also of independent interest.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in wave equations.
