BMO Estimates for Quasilinear Elliptic Equations with BMO Coefficients
Received:March 19, 2016  Revised:July 06, 2016
Key Word: Calder\'{o}n-Zygmund theory   Quasilinear elliptic equations   BMO space  
Fund ProjectL: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 NameAffiliation
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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