33 citations · 60 across the 14 of their papers we have counts for
14 papers
Classification of solutions to the singular Liouville's equation associated with the Finsler Laplacian
Jianwei Xue, Maochun Zhu
In this paper, we classify a class of singular Liouville's equation associated with the Finsler--Laplacian for any \begin{align*} -\mathrm{div}\left(F^{N-1}(\nabla…
Optimal concentration level of anisotropic Trudinger-Moser functionals on any bounded domain
Lu Chen, Rou Jiang, Maochun Zhu
Let be convex and homogeneous of degree , its polar represent a finsler metric on , and be any bounded open set in . In this pape…
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…
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…
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…
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…
Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg Groups and existence of ground state solutions
Jungang Li, Guozhen Lu, Maochun Zhu
Let be the -dimensional Heisenberg group, be the homogeneous dimension of . We extend the well-known con…
A sharp Trudinger-Moser type inequality involving norm in the entire space
Guozhen Lu, Maochun Zhu
Let be the standard Sobolev space and be the norm on . We establish a sharp form of the followi…
Interior HW^{1,p} estimates for divergence degenerate elliptic systems in Carnot groups
Maochun Zhu, Marco Bramanti, Pengcheng Niu
Let X_1,...,X_q be the basis of the space of horizontal vector fields on a homogeneous Carnot group in R^n (q<n). We consider a degenerate elliptic system of N equations, in diverg…
Estimates in Generalized Morrey Spaces for Weak Solutions to Divergence Degenerate Parabolic Systems
Yan Dong, Maochun Zhu, Pengcheng Niu
Let be a family of real smooth vector fields satisfying Hömander's condition. The purpose of this paper is to establish gradient estimates in general…
L^p and Schauder estimates for nonvariational operators structured on Hörmander vector fields with drift
Marco Bramanti, Maochun Zhu
We consider linear second order nonvariational partial differential operators of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the X_{i}'s (i=0,1,2,...,q, n>…
Local real analysis in locally homogeneous spaces
Marco Bramanti, Maochun Zhu
We introduce the concept of locally homogeneous space, and prove in this context L^p and Holder estimates for singular and fractional integrals, as well as L^p estimates on the com…