7 papers
Sharp quantitative stability of the Ashbaugh--Benguria inequality
Long-Han Huang, Yuxuan Zhou, Wenming Zou
We establish sharp quantitative stability of the Ashbaugh--Benguria inequality on bounded convex domains in . After volume and centroid normalization, the eigenvalue-r…
Sharp quantitative stability of the Hong--Krahn--Szegő inequality
Yuxuan Zhou, Wenming Zou
We establish sharp quantitative stability estimates for the Hong--Krahn--Szegő inequality for arbitrary open sets of positive finite measure in , . In dimension…
Interior Regularity for Stable Solutions of Semilinear Elliptic Equations with Sign-Changing Nonlinearities
Long-Han Huang, Yuxuan Zhou, Wenming Zou
We investigate interior regularity for stable solutions of the semilinear elliptic equation in an open set , where is locally Lipschitz and m…
Degenerate stability of critical points of the Caffarelli-Kohn-Nirenberg inequality along the Felli-Schneider curve
Yuxuan Zhou, Wenming Zou
In this paper, we investigate the validity of a quantitative version of stability for the critical Hardy-Hénon equation \begin{equation*} H(u):=÷(|x|^{-2a}\nabla u)+|x|^{-pb}|u|^{p…
The stability on the Caffarelli-Kohn-Nirenberg and Hardy-type inequalities and beyond
Yuxuan Zhou, Wenming Zou
In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts. In the first part, we consider the…
Classification of positive solutions to the Hénon-Sobolev critical systems
Yuxuan Zhou, Wenming Zou
In this paper, we investigate positive solutions to the following Hénon-Sobolev critical system: $$ -\mathrm{div}(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u+να|x|^{-bp}|u|^{α-2}|v|^βu\…
Sharp quantitative stability for the fractional Sobolev trace inequality
Yingfang Zhang, Yuxuan Zhou, Wenming Zou
In this paper, we study the stability of fractional Sobolev trace inequality within both the functional and critical point settings. In the functional setting, we establish the fol…