  The geometric properties of domains are well-known to be crucial factors
influencing the regularity of Boltzmann boundary problems. In the presence of
non-convex physical boundaries, highly singular behaviors are investigated
including the propagation of discontinuities \cite{Kim11} and H\"older
regularity \cite{CD2022}. In this paper, we focus on studying the
$C^{0,\frac{1}{4}-}$ H\"older regularity of the Boltzmann equation within
concentric cylinders where both convex and concave features are present on the
boundaries. Our findings extend the previous results of \cite{CD2022}, which
primarily addressed concavity while considering the exterior of convex objects.
