Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients

@article{Tian2017LorentzEF,
  title={Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients},
  author={Hong Xiang Tian and Shenzhou Zheng},
  journal={Boundary Value Problems},
  year={2017},
  volume={2017},
  pages={1-27}
}
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the leading coefficients are measurable in one variable and have small BMO semi-norms in the other variables, variable exponents p(x)$p(x)$ satisfy log-Hölder continuity, and the boundaries of domains are so-called Reifenberg flat. This is a natural outgrowth of the classical Calder… CONTINUE READING
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