@article{f0ab016e08f042b186e774f26a3eaf41,
title = "Green function estimates for second order elliptic operators in non-divergence form with Dini continuous coefficients",
abstract = "Two-sided sharp Green function estimates are obtained for second order uniformly elliptic operators in non-divergence form with Dini continuous coefficients in bounded C1,1 domains, which are shown to be comparable to that of the Dirichlet Laplace operator in the domain. The first and second order derivative estimates of the Green functions are also derived. Moreover, boundary Harnack inequality with an explicit boundary decay rate and interior Schauder{\textquoteright}s estimates for these differential operators are established, which may be of independent interest.",
keywords = "Green function, Martin integral representation, boundary Har-nack principle, harmonic function, interior Schauder{\textquoteright}s estimate",
author = "Chen, {Zhen Qing} and Wang, {Jie Ming}",
note = "Publisher Copyright: {\textcopyright} 2023, Institute of Mathematical Statistics. All rights reserved.",
year = "2023",
doi = "10.1214/23-EJP925",
language = "English",
volume = "28",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
}