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

Dong, Hongjie; Kim, Seick; Lee, Sungjin

doi:10.1090/proc/16326

Note on Green’s functions of non-divergence elliptic operators with continuous coefficients
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by Hongjie Dong, Seick Kim and Sungjin Lee;

Proc. Amer. Math. Soc. 151 (2023), 2045-2055

DOI: https://doi.org/10.1090/proc/16326

Published electronically: February 17, 2023

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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 $x_0$ as that of the corresponding Green’s function for the elliptic equation with constant coefficients frozen at $x_0$.

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