JournalszaaVol. 25 , No. 1DOI 10.4171/zaa/1276

Compactness and Sobolev-Poincaré Inequalities for Solutions of Kinetic Equations

  • Myriam Lecumberry

    Mathematik in den Naturwissenschaften, Leipzig, Germany
Compactness and Sobolev-Poincaré Inequalities for Solutions of Kinetic Equations cover

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} Ws,pW^{s,p}, 0<s<1p0<s<\frac{1}{p}, p[1,+)p\in[1,+\infty), in the velocity variable. Namely, the velocity averages have the same Sobolev regularity in the time-space variable.