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}
}