  The problem of determining the domain of the closure of the Laplace-Beltrami
operator on a 2D almost-Riemannian manifold is considered. Using tools from
theory of Lie groupoids natural domains of perturbations of the
Laplace-Beltrami operator are found. The main novelty is that the presented
method allows us to treat geometries with tangency points. This kind of
singularity is difficult to treat since those points do not have a tubular
neighbourhood compatible with the almost-Riemannian metric.
