Maximal regularity via reverse Hölder inequalities for elliptic systems of$n$-Laplace type involving measures

Tero Kilpeläinen Department of Mathematics and Statistics, University of Jyväskylä Nageswari Shanmugalingam Department of Mathematical Sciences, University of Cincinnati Xiao Zhong Department of Mathematics and Statistics, University of Jyväskylä

TBD mathscidoc:1701.333126

Arkiv for Matematik, 46, (1), 77-93, 2006.11
In this note, we consider the regularity of solutions of the nonlinear elliptic systems of$n$-Laplacian type involving measures, and prove that the gradients of the solutions are in the weak Lebesgue space$L$^{$n$,∞}. We also obtain the$a priori$global and local estimates for the$L$^{$n$,∞}-norm of the gradients of the solutions without using BMO-estimates. The proofs are based on a new lemma on the higher integrability of functions.
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@inproceedings{tero2006maximal,
  title={Maximal regularity via reverse Hölder inequalities for elliptic systems of$n$-Laplace type involving measures},
  author={Tero Kilpeläinen, Nageswari Shanmugalingam, and Xiao Zhong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203622220849935},
  booktitle={Arkiv for Matematik},
  volume={46},
  number={1},
  pages={77-93},
  year={2006},
}
Tero Kilpeläinen, Nageswari Shanmugalingam, and Xiao Zhong. Maximal regularity via reverse Hölder inequalities for elliptic systems of$n$-Laplace type involving measures. 2006. Vol. 46. In Arkiv for Matematik. pp.77-93. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203622220849935.
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