Two-sided sharp Green function estimates are obtained for second order uniformly elliptic operators in non-divergence form with Dini continuous coefficients in bounded 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’s estimates for these differential operators are established, which may be of independent interest.
The research of Z.-Q. Chen is supported in part by a Simons Foundation Grant. The research of J.-M. Wang is supported by NNSFC Grant 11731009.
We thank the referee for helpful comments of the paper.
"Green function estimates for second order elliptic operators in non-divergence form with Dini continuous coefficients." Electron. J. Probab. 28 1 - 54, 2023. https://doi.org/10.1214/23-EJP925