  In this short note, we prove an $L^6$-control of the macroscopic part of the
linear Boltzmann and Landau equations. This result is an extension of the test
function method of Esposito-Guo-Kim-Marra~\cite{EGKM}\cite{EGKM2} to the
specular reflection boundary condition, in which we crucially used the Korn's
inequality \cite{DV2} and the system of symmetric Poisson equations
\cite{Bernou}.
