Y. Zhang

activity

20162023

most citedA Variational Characterisation of the Second Eigenvalue of the p-Laplacian on Quasi Open Sets

6 citations · 11 across the 7 of their papers we have counts for

collaborators

11 papers

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.CV2020

Duality of capacities and Sobolev extendability in the plane

Yi Ru-Ya Zhang

We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions inv…

math.CV2019★ 2 cited

Ahlfors reflection theorem for $p$ -morphisms

Pekka Koskela, Pekka Pankka, Yi Ru-Ya Zhang

We prove an Ahlfors refection theorem for $p$ -reflections over Jordan curves bounding subhyperbolic domains in $C^$ .

math.OC2019

Strong stability for the Wulff inequality with a crystalline norm

Alessio Figalli, Yi Ru-Ya Zhang

Let $K$ be a convex polyhedron and $F$ its Wulff energy, and let $C (K)$ denote the set of convex polyhedra close to $K$ whose faces are parallel to those of $K$ .…

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…

math.AP2018★ 1 cited

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…

math.AP2018★ 6 cited

A Variational Characterisation of the Second Eigenvalue of the p-Laplacian on Quasi Open Sets

Nicola Fusco, Shirsho Mukherjee, Yi Ru-Ya Zhang

In this article, we prove a minimax characterization of the second eigenvalue of the p-Laplacian operator on p-quasi-open sets, using a construction based on minimizing movements.…

math.FA2016

A density problem for Sobolev spaces on Gromov hyperbolic domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

We prove that for a bounded domain $Ω \subset R^{n}$ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when $Ω$ is a finitely connected planar…

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

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