Sharp $L^1$ estimates for singular transport equations

Klainerman, Sergiu, and Rodnianski, Igor. "Sharp $L^1$ estimates for singular transport equations." Journal of the European Mathematical Society 010.2 (2008): 477-505. <http://eudml.org/doc/277280>.

@article{Klainerman2008,
abstract = {We provide $L^1$ estimates for a transport equation which contains singular integral operators. The form of the equation was motivated by the study of Kirchhoff–Sobolev parametrices in a Lorentzian space-time satisfying the Einstein equations. While our main application is for a specific problem in General Relativity we believe that the phenomenon which our result illustrates is of a more general interest.},
author = {Klainerman, Sergiu, Rodnianski, Igor},
journal = {Journal of the European Mathematical Society},
keywords = {Kirchhoff-Sobolev parametrices; Lorentzian space-time; Kirchhoff-Sobolev parametrices; Lorentzian space-time},
language = {eng},
number = {2},
pages = {477-505},
publisher = {European Mathematical Society Publishing House},
title = {Sharp $L^1$ estimates for singular transport equations},
url = {http://eudml.org/doc/277280},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Klainerman, Sergiu
AU - Rodnianski, Igor
TI - Sharp $L^1$ estimates for singular transport equations
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 477
EP - 505
AB - We provide $L^1$ estimates for a transport equation which contains singular integral operators. The form of the equation was motivated by the study of Kirchhoff–Sobolev parametrices in a Lorentzian space-time satisfying the Einstein equations. While our main application is for a specific problem in General Relativity we believe that the phenomenon which our result illustrates is of a more general interest.
LA - eng
KW - Kirchhoff-Sobolev parametrices; Lorentzian space-time; Kirchhoff-Sobolev parametrices; Lorentzian space-time
UR - http://eudml.org/doc/277280
ER -