Yuan Zhou

activity

20092022

most citedAnisotropic Singular Integrals in Product Spaces

27 citations · 119 across the 31 of their papers we have counts for

collaborators

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12 papers · 1 filter

math.AP2022★ 1 cited

Jacobian determinants for (nonlinear) gradient of planar $\infty$ -harmonic functions and applications

Hongjie Dong, Fa Peng, Yi Ru-Ya Zhang +1

In dimension 2, we introduce a distributional Jacobian determinant $det D V_{β} (D v)$ for the nonlinear complex gradient $(x_{1}, x_{2}) \mapsto ∣ D v ∣^{β} (v_{x_{1}}, - v_{x_{2}})$ for any $β > - 1$ , wh…

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…

math.AP2021★ 4 cited

Optimal regularity & Liouville property for stable solutions to semilinear elliptic equations in $R^{n}$ with $n \geq 10$

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

Let $0 \leq f \in C^{0, 1} (R^{n})$ . Given a domain $Ω \subset R^{n}$ , we prove that any stable solution to the equation $- Δ u = f (u)$ in $Ω$ satisfies a BMO interior regularit…

math.AP2019★ 1 cited

Second order regularity for elliptic and parabolic equations involving $p$ -Laplacian via a fundamental inequality

Hongjie Dong, Peng Fa, Yi Ru-Ya Zhang +1

Denote by $Δ$ the Laplacian and by $Δ_{\infty}$ the $\infty$ -Laplacian. A fundamental inequality is proved for the algebraic structure of $Δ v Δ_{\infty} v$ : for every $v \in C^{\infty}$ ,…

math.AP2019

C^1-Regularity of planar \infty-harmonic functions - REVISIT

Yi Ru-Ya Zhang, Yuan Zhou

In the seminal paper [Arch. Ration. Mech. Anal. 176 (2005), 351--361], Savin proved the $C^{1}$ -regularity of planar $\infty$ -harmonic functions $u$ . Here we give a new understanding…

Jacobian determinants for (nonlinear) gradient of planar ∞-harmonic functions and applications

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

Optimal regularity & Liouville property for stable solutions to semilinear elliptic equations in Rn with n≥10