33 citations · 56 across the 30 of their papers we have counts for
31 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…
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 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 equation in the two-dimensional Poincaré disk : \begin{equ…
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…
Trudinger-Moser and Hardy-Trudinger-Moser inequalities for the Aharonov-Bohm Magnetic field
Guozhen Lu, Qiaohua Yang
The main results of this paper concern sharp constant of the Trudinger-Moser inequality in for Aharonov-Bohm magnetic fields. This is a borderline case of the Hard…
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…
Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities
Cristian Cazacu, Joshua Flynn, Nguyen Lam +1
We set up a one-parameter family of inequalities that contains both the Hardy inequalities (when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the parame…
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…
Symmetry of solutions to higher and fractional order semilinear equations on hyperbolic spaces
Jungang Li, Guozhen Lu, Jianxiong Wang
We show that nontrivial solutions to higher and fractional order equations with certain nonlinearity are radially symmetric and nonincreasing on geodesic balls in the hyperbolic sp…
The Chang-Marshall Trace Inequality for Sobolev functions in domains in higher dimensional space
Jungang Li, Guozhen Lu
In their celebrated work [5], Chang and Marshall established a critical trace inequality of Moser-Trudinger type for holomorphic functions with mean value zero on unit disc in the…
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…
Higher order Brezis-Nirenberg problem on hyperbolic spaces: Existence, nonexistence and symmetry of solutions
Jungang Li, Guozhen Lu, Qiaohua Yang
The main purpose of this paper is to establish the existence, nonexistence and symmetry of nontrivial solutions to the higher order Brezis-Nirenberg problems associated with the GJ…
Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on quaternionic hyperbolic spaces and the Cayley hyperbolic plane
Joshua Flynn, Guozhen Lu, Qiaohua Yang
Though Adams and Hardy-Adams inequalities can be extended to general symmetric spaces of noncompact type fairly straightforwardly by following closely the systematic approach devel…
Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on the Siegel domains and complex hyperbolic spaces
Guozhen Lu, Qiaohua Yang
This paper continues the program initiated in the works by the authors [60], [61] and [62] and by the authors with Li [51] and [52] to establish higher order Poincaré-Sobolev, Hard…
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…