33 citations · 43 across the 18 of their papers we have counts for
20 papers
Attainment of the sharp stability constant of Beckner conformal log-Sobolev inequality
Lu Chen, Bohan Wang
The existence of minimizer for stability of the fractional Sobolev inequality and the stability of Beckner conformal Log-Sobolev inequality (the endpoint case of fractional Sobolev…
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…
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_Ω\lef…
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}} { - Δ_n u = λe^u} & {\rm in} \ \ Ω, \\ {\ \ \ \ u = 0} &\ {…
Optimal stability of Hardy-Littlewood-Sobolev and Sobolev inequalities of arbitrary orders with dimension-dependent constants
Lu Chen, Guozhen Lu, Hanli Tang
Recently, Dolbeault-Esteban-Figalli-Frank-Loss [20] established the optimal stability of the first-order -Sobolev inequality with dimension-dependent constant. Subsequently, C…
Optimal asymptotic lower bound for stability of fractional Sobolev inequality and the stability of Log-Sobolev inequality on the sphere
Lu Chen, Guozhen Lu, Hanli Tang
We establish the optimal asymptotic lower bound for the stability of fractional Sobolev inequality: \begin{equation}\label{Sob sta ine} \left\|(-Δ)^{s/2} U \right\|_2^2 - \mathcal…
A sharp trace Adams' inequality in and Existence of the extremals
Lu Chen, Guozhen Lu, Maochun Zhu
Let be a bounded domain with smooth boundary . In this paper, we establish the following sharp form of the trace Adams' inequality in $W^{2,2…
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth
Lu Chen, Guozhen Lu, Caifeng Zhang
In the past few decades, much attention has been paid to the bubbling problem for semilinear Neumann elliptic equation with the critical and subcritical polynomial nonlinearity, mu…
Stability of Hardy-Littlewood-Sobolev inequalities with explicit lower bounds
Lu Chen, Guozhen Lu, Hanli Tang
In this paper, we establish the stability for the Hardy-Littlewood-Sobolev (HLS) inequalities with explicit lower bounds. By establishing the relation between the stability of HLS…
Uniqueness of positive solutions to elliptic equations with the critical exponential growth on the unit disc and its applications
Lu Chen, Guozhen Lu, Ying Xue +1
In this paper, we will solve this uniqueness problem of positive solutions to the following equations of exponential growth: \begin{equation*} \begin{cases} -Δu =λue^{u^2},\quad\qu…
Sharp Stability of Log-Sobolev and Moser-Onofri inequalities on the Sphere
Lu Chen, Guozhen Lu, Hanli Tang
In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere . Namely, we will establis…
Existence and Non-existence of Ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials
Lu Chen, Guozhen Lu, Maochun Zhu
Recently, the authors of the current paper established in [9] the existence of a ground-state solution to the following bi-harmonic equation with the constant potential or Rabinowi…
Sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the upper half spaces
Lu Chen, Guozhen Lu, Qiaohua Yang +1
In this paper, we establish the sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the half spaces and prove the existence of their extremals through th…
Sharp subcritical Sobolev inequalities and uniqueness of nonnegative solutions to high-order Lane-Emden equations on
Lu Chen, Guozhen Lu, Yansheng Shen
In this paper, we are concerned with the uniqueness result for non-negative solutions of the higher-order Lane-Emden equations involving the GJMS operators on . Since…
Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials
Lu Chen, Guozhen Lu, Maochun Zhu
In this paper, we first give a necessary and sufficient condition for the boundedness and the compactness for a class of nonlinear functionals in . Using this…
Existence and Nonexistence of Extremals for critical Adams inequalities in R4 and Trudinger-Moser inequalities in R2
Lu Chen, Guozhen Lu, Maochun Zhu
Though much work has been done with respect to the existence of extremals of the critical first order Trudinger-Moser inequalities in and higher order Adams…
Stein-Weiss inequalities with the fractional Poisson kernel
Lu Chen, Zhao Liu, Guozhen Lu +1
In this paper, we establish the following Stein-Weiss inequality with the fractional Poisson kernel (see Theorem 1.1): \begin{equation}\label{int1} \int_{\mathbb{R}^n_{+}}\int_{\pa…
Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group
Lu Chen, Guozhen Lu, Chunxia Tao
In this paper, we establish the existence of extremals for two kinds of Stein-Weiss inequalities on the Heisenberg group. More precisely, we prove the existence of extremals for th…