A real space method for averaging lemmas

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Abstract

We introduce a new method to prove averaging lemmas, i.e., prove a regularizing effect on the average in velocity of a solution to a kinetic equation. The method does not require the use of Fourier transform and the whole procedure is performed in the 'real space'. We are consequently able to improve the known result when the integrability of the solution (or the right-hand side of the equation) is different in space and in velocity. We also present a few counterexamples to test the optimality of the new results.

Original languageEnglish (US)
Pages (from-to)1309-1351
Number of pages43
JournalJournal des Mathematiques Pures et Appliquees
Volume83
Issue number11
DOIs
StatePublished - Nov 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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