Green's function for nondivergence elliptic operators in two dimensions

Hongjie Dong, Seick Kim

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We construct the Green function for second-order elliptic equations in nondivergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that Green's function is a bounded mean oscillation in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of Green's function.

Original languageEnglish
Pages (from-to)4637-4656
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Issue number4
Publication statusPublished - 2021

Bibliographical note

Funding Information:
∗Received by the editors March 5, 2020; accepted for publication (in revised form) June 1, 2021; published electronically August 19, 2021. Funding: The work of the first author was partially supported by the National Science Foundation grant DMS-1600593. The work of the second author was partially supported by the National Research Foundation of Korea (NRF) grants NRF-20151009350 and NRF-2019R1A2C2002724. †Division of Applied Mathematics, Brown University, Providence, RI 02912 USA (Hongjie Dong@ ‡Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea (kimseick@

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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