# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsmathscidoc:1912.431017

arXiv preprint arXiv:1512.00629, 2015.12
We characterize probability measure with finite moment of any order in terms of the symmetric difference operators of their Fourier transforms. By using our new characterization, we prove the continuity f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) , where f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) stands for the density of unique measure-valued solution f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) of the Cauchy problem for the homogeneous non-cutoff Boltzmann equation, with Maxwellian molecules, corresponding to a probability measure initial datum f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) satisfying$\int| v|^{2k-2+ } dF_0 (v)&lt;\infty, 0\leq &lt; 2, k= 2, 3, 4,\cdots$ provided that f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) is not a single Dirac mass.
@inproceedings{yong-kum2015a,