6 papers
Sharp stability of Alexandrov's theorem for 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 open sets in a small-excess regime. More precisely, if $E\subset \m…
Planar -extension domains
Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang
We show that a bounded planar simply connected domain is a -extension domain if and only if for every pair of points in there exists a curve $γ\subset…
Geometric properties of Euclidean domains supporting trace inequalities
Weicong Su, Zhuang Wang, Yi Ru-Ya Zhang
We investigate the geometric behavior of for bounded finite-perimeter sets , where is the trace constant introduced by Figalli--Maggi--Pratel…
Serrin's overdetermined theorem within Lipschitz domains
Hongjie Dong, Yi Ru-Ya Zhang
Let be a Lipschitz domain. We prove that, satisfies the following Serrin-type overdetermined system $$u \in W^{1,2}(\mathbb R^n), \quad u=0\ \text{ a.e.…
Sharp stability for critical points of the Sobolev inequality in the absence of bubbling
Gemei Liu, Yi Ru-Ya Zhang
When is close to a single Talenti bubble of the -Sobolev inequality, we show that \begin{equation*} \|Du-Dv\|_{L^p(\mathbb{R}^n)}^{\max\{1,p-1\}}\le C \|-{\rm div}(|Du|^…
A growth estimate for the planar Mumford--Shah minimizers at a tip point: An alternative proof of David--Léger
Yi Ru-Ya Zhang
Let be a bounded domain and be a local minimizer of the Mumford--Shah problem in the plane, with being a tip point and…