Gradient regularity for elliptic equations in the Heisenberg group

@inproceedings{Mingione2009GradientRF,
  title={Gradient regularity for elliptic equations in the Heisenberg group},
  author={Giuseppe Mingione and Anna Zatorska-Goldstein and Xiao Ling Zhong},
  year={2009}
}
We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised in [40], where only dimension dependent bounds for the growth exponent are given. We also obtain explicit a priori local regularity estimates, and cover the case of the horizontal pLaplacean operator, extending some regularity proven in [17]. In turn, the a priori estimates found… CONTINUE READING

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