Yi-Ru-Ya Zhang

activity

20152026

most citedA density problem for Sobolev spaces on planar domains

10 citations · 21 across the 20 of their papers we have counts for

collaborators

20 papers

math.CV2026

A sharp stability inequality of Liouville's theorem for quasiregular mappings on bounded domains

Yi Ru-Ya Zhang

Let $n \geq 3$ and fix $p > n$ . We establish a sharp quantitative stability result in $W^{1, p}$ for Liouville's theorem for nonconstant, sense-preserving quasiregular mappings whose o…

math.AP2026

An Almgren-type formula for planar $p$ -harmonic functions

Yi Ru-Ya Zhang

For a nonconstant planar $p$ -harmonic function $u$ , with $1 < p < \infty$ , and according to previous results, most notably Aronsson's fundamental analysis of the hodograph represen…

math.AP2026

Critical $p$ -Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality

Yi Ru-Ya Zhang

We investigate positive weak solutions of the critical $p$ -Laplace equation $- Δ_{p} u = u^{p^{*} - 1} h (u), 1 < p < n,$ where $h$ is a positive, bounded, continuous, and nonin…

math.AP2026

Strictly stable solutions in uniformly convex planar domains may have nonconvex superlevel sets

Yi Ru-Ya Zhang

We construct smooth, uniformly convex planar domains that admit minimal, strictly stable solutions of a semilinear Dirichlet problem whose superlevel sets are nonetheless nonconvex…

math.DG2026

Sharp stability of Alexandrov's theorem for $C^{1}$ domains in the small-excess regime

Alessio Figalli, Yi Ru-Ya Zhang

We prove a sharp quantitative stability result for Alexandrov's theorem in arbitrary dimension for bounded $C^{1}$ open sets in a small-excess regime. More precisely, if $E\subset \m…

math.AP2026

Global regularity and free boundary geometry in the planar Choné-Rochet model

Shibing Chen, Alessio Figalli, Yi Ru-Ya Zhang

In this paper, we study minimizers of the Choné--Rochet variational problem in dimension two. We first establish global $C^{1}$ regularity on arbitrary bounded convex domains, and th…

math.AP2026

An anisotropic Serrin's problem in general domains

Alessio Figalli, Yi Ru-Ya Zhang

Serrin's symmetry theorem shows that the classical overdetermined torsion problem forces the domain to be a ball. Extending this rigidity statement to merely Lipschitz (and more ge…

math.FA2025

Planar $W^{1, 1}$ -extension domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

We show that a bounded planar simply connected domain $Ω$ is a $W^{1, 1}$ -extension domain if and only if for every pair $x, y$ of points in $Ω^{c}$ there exists a curve $γ\subset Ω^…

math.AP2024

Serrin's overdetermined problem in rough domains

Alessio Figalli, Yi Ru-Ya Zhang

The classical Serrin's overdetermined theorem states that a $C^{2}$ bounded domain, which admits a function with constant Laplacian that satisfies both constant Dirichlet and Neumann…

math.OC2024

Sobolev trace inequalities on John domains and its applications

Weicong Su, Yi Ru-Ya Zhang

We prove that a trace inequality holds for John domains $Ω$ satisfying $H^{n - 1} (\partial Ω ∖ \partial_{*} Ω) = 0,$ where $\partial_{*} Ω$ denotes the measure-theoretic b…

math.OC2024

Carrot John domains in variational problems

Weicong Su, Yi Ru-Ya Zhang

In this paper, we explore carrot John domains within variational problems, dividing our examination into two distinct sections. The initial part is dedicated to establishing the lo…

math.OC2023

Strong stability of convexity with respect to the perimeter

Alessio Figalli, Yi Ru-Ya Zhang

Let $E \subset R^{n}$ , $n \geq 2$ , be a set of finite perimeter with $∣ E ∣ = ∣ B ∣$ , where $B$ denotes the unit ball. When $n = 2$ , since convexification decreases perimeter (in the cl…

math.AP2021

Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations

Alessio Figalli, Yi Ru-Ya Zhang

We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well-known that: - For $n = 2$ , there exist Morse index $1$ solu…

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.FA2020★ 2 cited

Sharp gradient stability for the Sobolev inequality

Alessio Figalli, Yi Ru-Ya Zhang

We prove a sharp quantitative version of the $p$ -Sobolev inequality for any $1 < p < n$ , with a control on the strongest possible distance from the class of optimal functions. Surprisi…

math.CV2018

Schoenflies solutions of conformal boundary values may fail to be Sobolev

Yi Ru-Ya Zhang

We show that there exists a planar Jordan domains $Ω$ with boundary of Hausdorff dimension $1$ such that, for any conformal maps $φ : D \to Ω$ , any homeomorphic extensi…

math.AP2018

Some sharp Sobolev regularity for inhomogeneous $\infty$ -Laplace equation in plane

Herbert Koch, Yi Ru-Ya Zhang, Yuan Zhou

Suppose $Ω ⋐ R^{2}$ and $f \in B V_{l oc} (Ω) \cap C^{0} (Ω)$ with $∣ f ∣ > 0$ in $Ω$ . Let $u \in C^{0} (Ω)$ be a viscosity solution to the inhomogeneous $\infty$ -Laplace equation $$ -Δ…

math.FA2016★ 1 cited

A quasiconformal composition problem for the Q-spaces

Pekka Koskela, Jie Xiao, Yi Ru-Ya Zhang +1

Given a quasiconformal mapping $f : R^{n} \to R^{n}$ with $n \geq 2$ , we show that (un-)boundedness of the composition operator $C_{f}$ on the spaces $Q_{α} (R^{n})$ de…

math.CA2015★ 10 cited

A density problem for Sobolev spaces on planar domains

Pekka Koskela, Yi Ru-Ya Zhang

We prove that for a bounded simply connected domain $Ω \subset R^{2}$ , the Sobolev space $W^{1, \infty} (Ω)$ is dense in $W^{1, p} (Ω)$ for any $1 \leq p < \infty$ . Moreover, we s…

math.CA2015★ 4 cited

A geometric characterization of planar Sobolev extension domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

We characterize bounded simply-connected planar $W^{1, p}$ -extension domains for $1 < p < 2$ as those bounded domains $Ω \subset R^{2}$ for which any two points $z_1,z_2 \in \ma…

A sharp stability inequality of Liouville's theorem for quasiregular mappings on bounded domains

An Almgren-type formula for planar p-harmonic functions

Critical p-Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality

Strictly stable solutions in uniformly convex planar domains may have nonconvex superlevel sets

Sharp stability of Alexandrov's theorem for C1 domains in the small-excess regime

Global regularity and free boundary geometry in the planar Choné-Rochet model

An anisotropic Serrin's problem in general domains

Planar W1,1-extension domains

Serrin's overdetermined problem in rough domains

Sobolev trace inequalities on John domains and its applications

Carrot John domains in variational problems

Strong stability of convexity with respect to the perimeter

Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations

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

Sharp gradient stability for the Sobolev inequality

Schoenflies solutions of conformal boundary values may fail to be Sobolev

Some sharp Sobolev regularity for inhomogeneous ∞-Laplace equation in plane

A quasiconformal composition problem for the Q-spaces

A density problem for Sobolev spaces on planar domains

A geometric characterization of planar Sobolev extension domains

An Almgren-type formula for planar $p$ -harmonic functions

Critical $p$ -Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality

Sharp stability of Alexandrov's theorem for $C^{1}$ domains in the small-excess regime

Planar $W^{1, 1}$ -extension domains

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

Some sharp Sobolev regularity for inhomogeneous $\infty$ -Laplace equation in plane