$HW^{2,2}_{\rm loc}$-regularity for $p$-harmonic functions in Heisenberg groups

Jiayin Liu; Fa Peng; Yuan Zhou

$HW^{2,2}_{\rm loc}$-regularity for $p$-harmonic functions in Heisenberg groups

Analysis of PDEs 2021-12-16 v1

Authors: Jiayin Liu , Fa Peng , Yuan Zhou

Abstract

Let $1<p\le4$ when $n=1$ and $1<p< 3+\frac{1}{n-1}$ when $n\ge2$ . We obtain the second-order horizontal Sobolev $HW^{2,2}_{\rm loc}$ -regularity of $p$ -harmonic functions in the Heisenberg group $\mathbb H^n$ . This improves the known range of $p$ obtained by Domokos and Manfredi in 2005.

Keywords

p-harmonic functions heisenberg group sobolev regularity horizontal sobolev space partial differential equations

Cite

@article{arxiv.2112.07908,
  title  = {$HW^{2,2}_{\rm loc}$-regularity for $p$-harmonic functions in Heisenberg groups},
  author = {Jiayin Liu and Fa Peng and Yuan Zhou},
  journal= {arXiv preprint arXiv:2112.07908},
  year   = {2021}
}

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