$H{W}_{\mathrm{loc}}^{2,2}$-regularity for $p$-harmonic functions in Heisenberg groups

Jiayin Liu, Fa Peng, Yuan Zhou

Let $1<p\le 4$ when $n=1$ and $1<p<3+\frac{1}{n-1}$ when $n\ge 2$. We obtain the second-order horizontal Sobolev $H{W}_{\mathrm{loc}}^{2,2}$-regularity of $p$-harmonic functions in the H…