A Generalized Representation Formula for Systems of Tensor Wave Equations

Details A Generalized Representation Formula for Systems of Tensor Wave Equations A Generalized Representation Formula for Systems of Tensor Wave Equations

2010-05-25

arxiv.org/abs/1005.4509v1

Commun.Math.Phys.306:51-82,2011

Mathematics

Analysis of PDEs

29 pages

Scientific paper

10.1007/s00220-011-1273-2

In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization is a key component for extending Klainerman and Rodnianski's breakdown criterion result for Einstein-vacuum spacetimes to Einstein-Maxwell and Einstein-Yang-Mills spacetimes.

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