Nonlinear gradient estimates for double phase elliptic problems with irregular double obstacles
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- by Sun-Sig Byun, Shuang Liang and Shenzhou Zheng PDF
- Proc. Amer. Math. Soc. 147 (2019), 3839-3854 Request permission
Abstract:
An elliptic double phase problem with irregular double obstacles is investigated to establish a Calderón-Zygmund type estimate in the setting of Lebesgue spaces and weighted Lebesgue spaces. We prove that the gradient of a solution to such a highly nonlinear problem is as integrable as both the nonhomogeneous term in divergence form and the gradient of the associated double obstacles under minimal regularity requirements on the given nonlinear elliptic operator.References
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Additional Information
- Sun-Sig Byun
- Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
- MR Author ID: 738383
- Email: byun@snu.ac.kr
- Shuang Liang
- Affiliation: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
- MR Author ID: 1265570
- Email: shuangliang@bjtu.edu.cn
- Shenzhou Zheng
- Affiliation: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
- MR Author ID: 605970
- Email: shzhzheng@bjtu.edu.cn
- Received by editor(s): December 9, 2018
- Published electronically: April 9, 2019
- Additional Notes: The first author was supported by NRF-2017R1A2B2003877.
The second author was partially supported by NRF2015R1A4A1041675. - Communicated by: Joachim Krieger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3839-3854
- MSC (2010): Primary 35J70, 35B65
- DOI: https://doi.org/10.1090/proc/14532
- MathSciNet review: 3993776