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

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9 papers · 1 filter

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.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.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.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.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…

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

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

An anisotropic Serrin's problem in general domains

Serrin's overdetermined problem in rough domains

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

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

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

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

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