Sharp L1 estimates for singular transport equations

Sergiu Klainerman; Igor Rodnianski

doi:10.4171/JEMS/119

Sharp L¹ estimates for singular transport equations

Sergiu Klainerman, Igor Rodnianski

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	American English
Pages (from-to)	477-505
Number of pages	29
Journal	Journal of the European Mathematical Society
Volume	10
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/119
State	Published - 2008

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "Sharp L1 estimates for singular transport equations",

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.",

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AU - Klainerman, Sergiu

AU - Rodnianski, Igor

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AB - 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.

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DO - 10.4171/JEMS/119

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JO - Journal of the European Mathematical Society

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Sharp L¹ estimates for singular transport equations

Abstract

ASJC Scopus subject areas

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