7 papers
A complete characterization of the existence of extremals for the Trudinger-Moser inequality on under sharp -perturbations
Lu Chen, Rou Jiang, Guozhen Lu +1
In this paper, we investigate the following critical Trudinger--Moser inequality on under sharp -perturbations: $$ S(λ,p) := \sup_{\substack{u\in H^{1}(\mathbb R…
Stability for Critical Points of the Hardy--Littlewood--Sobolev Inequality and a Dual Stability Framework
Lu Chen, Guozhen Lu, Hanli Tang
Although quantitative stability for critical points of the Sobolev and fractional Sobolev inequalities has been extensively studied, the corresponding stability theory for critical…
Quantization analysis of Moser-Trudinger equations in the Poincaré disk and applications
Lu Chen, Qiaoqiao Hua, Guozhen Lu +2
In this paper, we first establish the quantitative properties for positive solutions to the Moser-Trudinger equations in the two-dimensional Poincaré disk : \begin{e…
Quantization property of n-Laplacian mean field equation and sharp Moser-Onofri inequality
Lu Chen, Guozhen Lu, Bohan Wang
In this paper, we are concerned with the following -Laplacian mean field equation \[ \left\{ {\begin{array}{*{20}{c}} { - Î_n u = λe^u} & {\rm in} \ \ Ω, \\ {\ \ \ \ u = 0} &…
Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants
Lu Chen, Guozhen Lu, Hanli Tang +1
In this paper, we are concerned with the optimal asymptotic lower bound for the stability of Sobolev inequality on the Heisenberg group. We first establish the optimal local stabil…
Existence and Nonexistence of Extremals for Trudinger-Moser inequalities with type perturbation on any bounded planar domains
Lu Chen, Rou Jiang, Guozhen Lu +1
In this study, we investigate the perturbed Trudinger-Moser inequalities as follows:\[ S_Ω(λ,p)=\sup_{u\in H_{0}^{1}(Ω),\Vert\nabla u\Vert _{L^{2}\left( Ω\right) }\leq 1}\int_΅