Jiayin Liu

most citedOn the Dimension of Kakeya Sets in the First Heisenberg Group

4 citations · 4 across the 5 of their papers we have counts for

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math.AP2021

$H W_{loc}^{2, 2}$ -regularity for $p$ -harmonic functions in Heisenberg groups

Jiayin Liu, Fa Peng, Yuan Zhou

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

math.AP2021

A quantitative second order estimate for (weighted) $p$ -harmonic functions in manifolds under curvature-dimension condition

Jiayin Liu, Shijin Zhang, Yuan Zhou

We build up a quantitative second order Sobolev estimate of $ln w$ for positive $p$ -harmonic functions $w$ in Riemannian manifolds under Ricci curvature bounded from blow and als…

HWloc2,2​-regularity for p-harmonic functions in Heisenberg groups

A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition

$H W_{loc}^{2, 2}$ -regularity for $p$ -harmonic functions in Heisenberg groups

A quantitative second order estimate for (weighted) $p$ -harmonic functions in manifolds under curvature-dimension condition