A real space method for averaging lemmas

Pierre Emmanuel Jabin; Luis Vega

doi:10.1016/j.matpur.2004.03.004

A real space method for averaging lemmas

Pierre Emmanuel Jabin, Luis Vega

Mathematics

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

24 Scopus citations

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	https://doi.org/10.1016/j.matpur.2004.03.004
State	Published - Nov 2004

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1016/j.matpur.2004.03.004

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title = "A real space method for averaging lemmas",

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.",

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AB - 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.

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JO - Journal des Mathematiques Pures et Appliquees

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A real space method for averaging lemmas

Abstract

All Science Journal Classification (ASJC) codes

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