Abstract
AbstractThis 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.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Università Politecnica delle Marche
Publisher
Springer Science and Business Media LLC
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