English

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

Analysis of PDEs 2023-02-24 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2302.11889,
  title  = {On the obstacle problem associated to the Kolmogorov-Fokker-Planck operator with rough coefficients},
  author = {Francesca Anceschi and Annalaura Rebucci},
  journal= {arXiv preprint arXiv:2302.11889},
  year   = {2023}
}