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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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 $x_0$.
References
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Bibliographic Information
  • Hongjie Dong
  • Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
  • MR Author ID: 761067
  • ORCID: 0000-0003-2258-3537
  • Email: Hongjie_Dong@brown.edu
  • Seick Kim
  • Affiliation: Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea
  • MR Author ID: 707903
  • ORCID: 0000-0002-1220-3257
  • Email: kimseick@yonsei.ac.kr
  • Sungjin Lee
  • Affiliation: Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea
  • MR Author ID: 1096676
  • ORCID: 0000-0002-2821-2676
  • Email: sungjinlee@yonsei.ac.kr
  • Received by editor(s): January 9, 2022
  • Received by editor(s) in revised form: September 3, 2022
  • Published electronically: February 17, 2023
  • Additional Notes: The first author was partially supported by the Simons Foundation, grant no. 709545, a Simons fellowship, grant no. 007638, and the NSF under agreement DMS-2055244.
    The second author was partially supported by National Research Foundation of Korea (NRF) Grant No. NRF-2019R1A2C2002724 and No. NRF-2022R1A2C1003322.
  • Communicated by: Ryan Hynd
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2045-2055
  • MSC (2020): Primary 35J08, 35B45; Secondary 35J47
  • DOI: https://doi.org/10.1090/proc/16326
  • MathSciNet review: 4556199