| BMO Estimates for Quasilinear Elliptic Equations with BMO Coefficients |
| Received:March 19, 2016 Revised:July 06, 2016 |
| Key Words:
Calder\'{o}n-Zygmund theory Quasilinear elliptic equations BMO space
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11401473), Fundamental Research Funds for the Central Universities (Grant No.31920160059), the Natural Science Foundation of Gansu Province (Grant Nos.1506RJYA272; 1506RJZA274), Science and Humanity Foundation of the Ministry of Education (Grant No.15YJA880085), Foundation of State Nationalities Affairs Commission (Grant No.14XBZ016) and Research and Innovation Teams of Northwest University for Nationalities. |
| Author Name | Affiliation | | Qiaoyu TIAN | School of Mathematics and Computer Science, Northwest University for Nationalities, Gansu 730030, P. R. China | | Shengzhi ZHANG | Department of Mathematics, Gansu Normal University for Nationalities, Gansu 747000, P. R. China | | Yonglin XU | School of Mathematics and Computer Science, Northwest University for Nationalities, Gansu 730030, P. R. China | | Jia MU | School of Mathematics and Computer Science, Northwest University for Nationalities, Gansu 730030, P. R. China |
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| Abstract: |
| We establish a global limiting case of nonlinear Calder\'{o}n-Zygmund theory to quasilinear elliptic equations ${\rm div}\,\mathcal {A}(x,D u)={\rm div}(|F|^{p-2}F)$ under the BMO smallness of the nonlinearity, that is $|F|^{p-2}F\in {\rm BMO}$ implies that $Du\in {\rm BMO}$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.06.006 |
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