English

Optimal regularity for degenerate Kolmogorov equations with rough coefficients

Analysis of PDEs 2023-05-04 v2

Abstract

We consider a class of degenerate equations satisfying a parabolic H\"ormander condition, with coefficients that are measurable in time and H\"older continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal H\"older regularity, as well as Gaussian estimates. These results are key to study the backward Kolmogorov equations associated to a class of Langevin-type diffusions.

Keywords

Cite

@article{arxiv.2204.14158,
  title  = {Optimal regularity for degenerate Kolmogorov equations with rough coefficients},
  author = {Giacomo Lucertini and Stefano Pagliarani and Andrea Pascucci},
  journal= {arXiv preprint arXiv:2204.14158},
  year   = {2023}
}

Comments

28 pages

R2 v1 2026-06-24T11:02:45.576Z