Compactness and Sobolev-Poincaré inequalities for solutions of kinetic equations (Q2492113)

Summary: We prove a regularity result on the velocity averages of the solution of a kinetic equation whose data have a Sobolev regularity \(W^{s,p}\), \(0<s<\frac 1p\), \(p\in[1,+\infty)\), in the velocity variable. Namely, the velocity averages have the same Sobolev regularity in the time-space variable.