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

On the obstacle problem associated to the Kolmogorov-Fokker-Planck operator with rough coefficients