A pointwise finite-dimensional reduction method for a fully coupled system of Einstein-Lichnerowicz type
Abstract
We construct non-compactness examples for the fully coupled Einstein-Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on a priori pointwise asymptotic techniques.
Cite
@article{arxiv.1605.05468,
title = {A pointwise finite-dimensional reduction method for a fully coupled system of Einstein-Lichnerowicz type},
author = {Bruno Premoselli},
journal= {arXiv preprint arXiv:1605.05468},
year = {2016}
}