Sharp estimates for singular transport equations

  • Sergiu Klainerman

    Princeton University, USA
  • Igor Rodnianski

    Massachusetts Institute of Technology, Cambridge, USA


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 verifying 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.

Cite this article

Sergiu Klainerman, Igor Rodnianski, Sharp estimates for singular transport equations. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 477–505

DOI 10.4171/JEMS/119