Note on Green's functions of non-divergence elliptic operators with continuous coefficients

Abstract

We improve a result in Kim and Lee (Ann. Appl. Math. 37(2):111--130, 2021): showing that if the coefficients of an elliptic operator in non-divergence form are of Dini mean oscillation, then its Green's function has the same asymptotic behavior near the pole $x_0$ as that of the corresponding Green's function for the elliptic equation with constant coefficients frozen at $x_0$.