Quantitative De Giorgi methods in kinetic theory
Analysis of PDEs
2022-07-13 v2
Abstract
We consider hypoelliptic equations of kinetic Fokker-Planck type, also known as Kolmogorov or ultraparabolic equations, with rough coefficients in the drift-diffusion operator. We give novel short quantitative proofs of the De Giorgi intermediate-value Lemma as well as weak Harnack and Harnack inequalities. This implies H{\"o}lder continuity with quantitative estimates. The paper is self-contained.
Cite
@article{arxiv.2103.09646,
title = {Quantitative De Giorgi methods in kinetic theory},
author = {Jessica Guerand and Clément Mouhot},
journal= {arXiv preprint arXiv:2103.09646},
year = {2022}
}