Elliptic equations with matrix weights and measurable nonlinearities on nonsmooth domains
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- by Sun-Sig Byun, Yumi Cho and Ho-Sik Lee;
- Proc. Amer. Math. Soc. 152 (2024), 2963-2982
- DOI: https://doi.org/10.1090/proc/16770
- Published electronically: May 21, 2024
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Abstract:
We study general elliptic equations with singular/degenerate matrix weights and measurable nonlinearities on nonsmooth bounded domains to obtain a global Calderón-Zygmund type estimate under possibly minimal assumptions that the logarithm of the matrix weight has a small bounded mean oscillation (BMO) norm, the nonlinearity is allowed to be merely measurable in one variable but has a small BMO norm in the other variables and that the boundary of the domain is sufficiently flat in Reifenberg sense.References
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Bibliographic Information
- Sun-Sig Byun
- Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Korea
- MR Author ID: 738383
- Email: byun@snu.ac.kr
- Yumi Cho
- Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Korea
- MR Author ID: 992545
- ORCID: 0000-0002-9124-5614
- Email: imuy31@snu.ac.kr
- Ho-Sik Lee
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany
- MR Author ID: 1437299
- ORCID: 0000-0001-6133-0693
- Email: ho-sik.lee@uni-bielefeld.de
- Received by editor(s): June 20, 2022
- Received by editor(s) in revised form: December 25, 2023
- Published electronically: May 21, 2024
- Additional Notes: The first author was supported by NRF-2022R1A2C1009312. The second author was supported by NRF-2022R1I1A1A01063170. The third author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through (GRK 2235/2 2021 - 282638148) at Bielefeld University.
The second author is the corresponding author. - Communicated by: Ariel Barton
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2963-2982
- MSC (2020): Primary 35B65; Secondary 35J70, 35J75
- DOI: https://doi.org/10.1090/proc/16770
- MathSciNet review: 4753281