Yi Ru-Ya Zhang

collaborators

4 papers

math.FA2026

Geometric properties of Euclidean domains supporting trace inequalities

Weicong Su, Zhuang Wang, Yi Ru-Ya Zhang

We investigate the geometric behavior of $τ (E)$ for bounded finite-perimeter sets $E \subset R^{n}$ , where $τ (E)$ is the trace constant introduced by Figalli--Maggi--Pratelli…

math.AP2025

Serrin's overdetermined theorem within Lipschitz domains

Hongjie Dong, Yi Ru-Ya Zhang

Let $Ω \subset R^{n}$ be a Lipschitz domain. We prove that, $Ω$ satisfies the following Serrin-type overdetermined system $$u \in W^{1,2}(\mathbb R^n), \quad u=0\ \text{ a.e. i…

math.AP2025

Sharp stability for critical points of the Sobolev inequality in the absence of bubbling

Gemei Liu, Yi Ru-Ya Zhang

When $u$ is close to a single Talenti bubble $v$ of the $p$ -Sobolev inequality, we show that \begin{equation*} \|Du-Dv\|_{L^p(\mathbb{R}^n)}^{\max\{1,p-1\}}\le C \|-{\rm div}(|Du|^…

math.AP2025

A growth estimate for the planar Mumford--Shah minimizers at a tip point: An alternative proof of David--Léger

Yi Ru-Ya Zhang

Let $Ω \subset R^{2}$ be a bounded domain and $u \in S B V (Ω)$ be a local minimizer of the Mumford--Shah problem in the plane, with $0 \in S_{u}$ being a tip point and $B…