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 (2021), pp. 111–130], 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 x_0 as that of the corresponding Green’s function for the elliptic equation with constant coefficients frozen at x 0 x_0 .