Sharp Schauder Estimates for some Degenerate Kolmogorov Equations
Analysis of PDEs
2020-12-14 v2 Probability
Abstract
We provide here some sharp Schauder estimates for degenerate PDEs of Kolmogorov type when the coefficients lie in some suitable anisotropic H{\"o}lder spaces and the first order term is non-linear and unbounded. We proceed through a perturbative approach based on forward parametrix expansions. Due to the low regularizing properties of the degenerate variables, for the procedure to work, we heavily exploit duality results between appropriate Besov spaces. Our method can be seen as constructive and provides, even in the non-degenerate case, an alternative approach to Schauder estimates.
Cite
@article{arxiv.1810.12227,
title = {Sharp Schauder Estimates for some Degenerate Kolmogorov Equations},
author = {Paul-Eric Chaudru de Raynal and Igor Honoré and Stéphane Menozzi},
journal= {arXiv preprint arXiv:1810.12227},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1910.03653 by other authors