  This work is devoted to the study of the obstacle problem associated to the
Kolmogorov-Fokker-Planck operator with rough coefficients through a variational
approach. In particular, after the introduction of a proper anisotropic Sobolev
space and related properties, we prove the existence and uniqueness of a weak
solution for the obstacle problem by adapting a classical perturbation argument
to the convex functional associated to the case of our interest. Finally, we
conclude this work by providing a one-sided associated variational inequality,
alongside with an overview on related open problems.
