NOTE ON GREEN’S FUNCTIONS OF NON-DIVERGENCE ELLIPTIC OPERATORS WITH CONTINUOUS COEFFICIENTS

Hongjie Dong; Seick Kim; Sungjin Lee

doi:10.1090/proc/16326

NOTE ON GREEN’S FUNCTIONS OF NON-DIVERGENCE ELLIPTIC OPERATORS WITH CONTINUOUS COEFFICIENTS

Hongjie Dong, Seick Kim, Sungjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 x0 as that of the corresponding Green’s function for the elliptic equation with constant coefficients frozen at x0.

Original language	English
Pages (from-to)	2045-2055
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	5
DOIs	https://doi.org/10.1090/proc/16326
Publication status	Published - 2023 May 1

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© 2023 American Mathematical Society.

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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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{\textquoteright}s function has the same asymptotic behavior near the pole x0 as that of the corresponding Green{\textquoteright}s function for the elliptic equation with constant coefficients frozen at x0.",

keywords = "Dini mean oscillation, Green{\textquoteright}s function, non-divergence elliptic equation",

author = "Hongjie Dong and Seick Kim and Sungjin Lee",

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AU - Lee, Sungjin

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AB - 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 x0 as that of the corresponding Green’s function for the elliptic equation with constant coefficients frozen at x0.

KW - Dini mean oscillation

KW - Green’s function

KW - non-divergence elliptic equation

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NOTE ON GREEN’S FUNCTIONS OF NON-DIVERGENCE ELLIPTIC OPERATORS WITH CONTINUOUS COEFFICIENTS

Abstract

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