2012/04/08 by Jérémie Szeftel, Szeftel, Jeremie
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1204.1768
openalex publication_date 2012/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first of a sequence of four papers \citeparam1, \citeparam2, \citeparam3, \citeparam4 dedicated to the construction and the control of a parametrix to the homogeneous wave equation \square\bf g ϕ=0, where \bf 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 \bf R of \bf g is a major step of the proof of the bounded L2 curvature conjecture proposed in \citeKl:2000, and solved jointly with S. Klainerman and I. Rodnianski in \citeboundedl2. On a more general level, this sequence of papers 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.