A real space method for averaging lemmas
type: Item
instance of: scholarly article
title: A real space method for averaging lemmas
zbMATH Open document ID: 1082.35043
author: Pierre-Emmanuel Jabin
author: L. Vega
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2005-05-04T00:00:00Z
review text: The authors study the kinetic equation \[ v\cdot \nabla_x f (x,v)= \Delta^{\alpha/2} g (x,v)\, , \] where \(x\in {\mathbb R}^d\), \(v\in {\mathbb R}^d\) and \(\alpha\in [0,1]\). In particular they prove several results about the regularity of ``velocity averages'', i.e. of quantities like \[ \rho (x)= \int f(x,v)\phi (v)\, dv, \qquad \phi\in C^\infty_c ({\mathbb R}^d)\, . \] It was first observed in [\textit{F. Golse, B. Perthame} and \textit{R. Sentis}, C. R. Acad. Sci., Paris, Sér. I 301, 341--344 (1985; Zbl 0591.45007)] that \(\rho\) is more regular than \(f\), motivating a large number of subsequent works. The authors' results improve the known regularity of \(\rho\) when the integrability of the solutions is different in space and velocity. Moreover their method of proof completely avoids the use of Fourier transform or wavelet decomposition, in contrast with all the methods known so far.
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 2164949
zbMATH Keywords: X-ray transform
zbMATH Keywords: kinetic equation
zbMATH Keywords: velocity averages
MaRDI profile type: Publication
full work available at URL: j.matpur.2004.03.004
OpenAlex ID: W1984896804
Wikidata QID: Q124877805
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DOI: 10.1016/J.MATPUR.2004.03.004
description: scientific article; zbMATH DE number 2164949