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