# Compactness and Sobolev-Poincaré Inequalities for Solutions of Kinetic Equations

### Myriam Lecumberry

Mathematik in den Naturwissenschaften, Leipzig, Germany

## Abstract

In this paper, we prove a regularity result on the velocity averages of the solution of a kinetic equation whose data have a Sobolev regularity \vspace{-0.05cm} $W^{s,p}$, $0<s<\frac{1}{p}$, $p\in[1,+\infty)$, in the velocity variable. Namely, the velocity averages have the same Sobolev regularity in the time-space variable.

## Cite this article

Myriam Lecumberry, Compactness and Sobolev-Poincaré Inequalities for Solutions of Kinetic Equations. Z. Anal. Anwend. 25 (2006), no. 1, pp. 23–49

DOI 10.4171/ZAA/1276