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

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arxiv 2201.03764 v3 pith:5FYPHP36 submitted 2022-01-11 math.AP

Hongjie Dong , Seick Kim , Sungjin Lee This is my paper · ORCID
classification math.AP
keywords coefficientsellipticgreenfunctionnon-divergenceapplasymptoticbehavior
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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 $x_0$.

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