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A Counter Example to Cercignani’s Conjecture for the d Dimensional Kac Model
(SpringerJournal of Statistical Physics, 2012-08-21)
Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ...
Sharp trace inequalities for fractional Laplacians
(American Mathematical SocietyProceedings of the American Mathematical Society, 2012-04-05)
The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on Rⁿ and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb’s ...