Sharp L1 estimates for singular transport equations

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Abstract

We provide L1 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.

Original languageEnglish (US)
Pages (from-to)477-505
Number of pages29
JournalJournal of the European Mathematical Society
Volume10
Issue number2
DOIs
StatePublished - Jan 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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