On montre que le terme de gain de lʼopérateur de collision pour un gaz de molécules Maxwelliennes nʼinduit pas dʼaugmentation de lʼinformation de Fisher. Notre preuve est une variante de celle donnée par Villani dans 1998 [2], plus courte et basée sur des techniques de type Fourier plutôt que sur des estimations directes. La méthode utilisée sʼapplique aussi au cas des convolutions de Wild générales (non symétriques).
It is shown that the collisional gain operator for a Maxwell gas does not increase the Fisher information. Our proof is a variant of the one given by Villani in 1998 [2], but it is shorter and based on Fourier techniques rather than direct estimates. The method we use also applies to general (non-symmetric) Wild convolutions.
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@article{CRMATH_2012__350_1-2_107_0, author = {Matthes, Daniel and Toscani, Giuseppe}, title = {Variation on a theme by {Bobyl\"ev} and {Villani}}, journal = {Comptes Rendus. Math\'ematique}, pages = {107--110}, publisher = {Elsevier}, volume = {350}, number = {1-2}, year = {2012}, doi = {10.1016/j.crma.2011.12.010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2011.12.010/} }
TY - JOUR AU - Matthes, Daniel AU - Toscani, Giuseppe TI - Variation on a theme by Bobylëv and Villani JO - Comptes Rendus. Mathématique PY - 2012 SP - 107 EP - 110 VL - 350 IS - 1-2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2011.12.010/ DO - 10.1016/j.crma.2011.12.010 LA - en ID - CRMATH_2012__350_1-2_107_0 ER -
%0 Journal Article %A Matthes, Daniel %A Toscani, Giuseppe %T Variation on a theme by Bobylëv and Villani %J Comptes Rendus. Mathématique %D 2012 %P 107-110 %V 350 %N 1-2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2011.12.010/ %R 10.1016/j.crma.2011.12.010 %G en %F CRMATH_2012__350_1-2_107_0
Matthes, Daniel; Toscani, Giuseppe. Variation on a theme by Bobylëv and Villani. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 107-110. doi : 10.1016/j.crma.2011.12.010. http://archive.numdam.org/articles/10.1016/j.crma.2011.12.010/
[1] The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules, Sov. Sci. Rev. C Math. Phys., Volume 7 (1988), pp. 111-233
[2] Fisher information estimates for Boltzmannʼs collision operator, J. Math. Pures Appl., Volume 77 (1998), pp. 821-837
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