Journal of the
Korean Mathematical Society JKMS

We will investigate the point spectrum on the imaginary axis of
the linearized Boltzmann operator with an external-force potential
in an exterior domain, i.e., in a domain $\Omega\subset{\Bbb R}^3$
such that ${\Bbb R}^3\setminus (\Omega\cup\partial\Omega)$ is a
bounded domain. The boundary condition considered is the perfectly
reflective boundary condition. We suppose that the boundary
$\partial\Omega$ is a sufficiently smooth surface. The point
spectrum on the imaginary axis is only equal to \{0\}. However,
the null space varies with the common axes of symmetry of $\Omega$

Keywords: point spectrum, linearized Boltzmann operator, external potential, exterior domain

MSC numbers: 76P05, 45K05