Lp$L^{p}$-Estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth

@article{Sun2016LpLpEstimatesFQ,
  title={Lp\$L^\{p\}\$-Estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth},
  author={Bang-Cheng Sun and Zhi-Ming Liu and Qiang Li and Shenzhou Zheng},
  journal={Boundary Value Problems},
  year={2016},
  volume={2016},
  pages={1-18}
}
We prove an interior Lp$L^{p}$-estimate of X-gradient of weak solutions to a class of quasilinear subelliptic equations with VMO coefficients under controllable growth. Here, we use a reverse Hölder inequality and De Giorgi’s iteration to establish the boundedness of their weak solutions. Then a local Lp$L^{p}$-estimate of the X-gradient of the weak solutions is derived by way of the bootstrap argument. 
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