Y. Zhang

activity

20162023

most citedJacobian determinants for (nonlinear) gradient of planar

\infty

-harmonic functions and applications

1 citations · 1 across the 3 of their papers we have counts for

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7 papers · 1 filter

math.AP2023

Regularity from $p$ -harmonic potentials to $\infty$ -harmonic potentials in convex rings

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

The exploration of shape metamorphism, surface reconstruction, and image interpolation raises fundamental inquiries concerning the $C^{1}$ and higher-order regularity of $\infty$ -har…

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.AP2022

Interior Hölder regularity for stable solutions to semilinear elliptic equations up to dimension 5

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

Let $2 \leq n \leq 5$ . We establish an apriori interior Hölder regularity of $C^{2}$ -stable solutions to the semilinear equation $- Δ u = f (u)$ in any domain of $R^{n}$ for any nonlinearity $f…

math.AP2019

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…

math.AP2018

An asymtotic sharp Sobolev regularity for planar infinity harmonic functions

Herbert Koch, Yi Ru-Ya Zhang, Yuan Zhou

Given an arbitrary planar $\infty$ -harmonic function $u$ , for each $α > 0$ we establish a quantitative local $W^{1, 2}$ -estimate of $∣ D u ∣^{α}$ , which is sharp as $α \to 0$ . We also show t…

Regularity from p-harmonic potentials to ∞-harmonic potentials in convex rings

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