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 language | English (US) |
---|---|
Pages (from-to) | 1309-1351 |
Number of pages | 43 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 83 |
Issue number | 11 |
DOIs | |
State | Published - Nov 2004 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics