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.
|Number of pages||20|
|Journal||SIAM Journal on Mathematical Analysis|
|Publication status||Published - 2021|
Bibliographical noteFunding Information:
∗Received by the editors March 5, 2020; accepted for publication (in revised form) June 1, 2021; published electronically August 19, 2021. https://doi.org/10.1137/20M1323618 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@ brown.edu). ‡Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea (kimseick@ yonsei.ac.kr).
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics