Yi-Ru-Ya Zhang

activity

20182026

collaborators

8 papers

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.FA2020

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…

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

Sharp gradient stability for the Sobolev inequality

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