A new approach to sharp Moser–Trudinger and Adams type inequalities: a rearrangement-free argument

N Lam, G Lu - Journal of Differential Equations, 2013 - Elsevier
The main purpose of this paper is two-fold. On the one hand, we will develop a new
approach to establish sharp singular Moser–Trudinger and Adams type inequalities in …

[HTML][HTML] Sharp Moser–Trudinger inequality on the Heisenberg group at the critical case and applications

N Lam, G Lu - Advances in Mathematics, 2012 - Elsevier
Let H= Cn× R be the n-dimensional Heisenberg group, Q= 2n+ 2 be the homogeneous
dimension of H, Q′= QQ− 1, and [Formula: see text] be the homogeneous norm of ξ=(z, t)∈ …

Equivalence of critical and subcritical sharp Trudinger–Moser–Adams inequalities

N Lam, G Lu, L Zhang - Revista Matemática Iberoamericana, 2017 - ems.press
Abstract Sharp Trudinger–Moser inequalities on the first order Sobolev spaces and their
analogous Adams inequalities on high order Sobolev spaces play an important role in …

Sharpened Adams Inequality and Ground State Solutions to the Bi-Laplacian Equation in ℝ4

L Chen, J Li, G Lu, C Zhang - Advanced Nonlinear Studies, 2018 - degruyter.com
In this paper, we establish a sharp concentration-compactness principle associated with the
singular Adams inequality on the second-order Sobolev spaces in ℝ 4. We also give a new …

Sharp Adams type inequalities in Sobolev spaces Wm, nm (Rn) for arbitrary integer m

N Lam, G Lu - Journal of Differential Equations, 2012 - Elsevier
The main purpose of our paper is to prove sharp Adams type inequalities in unbounded
domains of Rn for the Sobolev space Wm, nm (Rn) for any positive integer m less than n …

On Nonuniformly Subelliptic Equations of Q− sub-Laplacian Type with Critical Growth in the Heisenberg Group

N Lam, G Lu, H Tang - Advanced Nonlinear Studies, 2012 - degruyter.com
Let ℍn= ℝ2n× ℝ be the n− dimensional Heisenberg group, be its subelliptic gradient
operator, and ρ (ξ)=(| z| 4+ t2) 1/4 for ξ=(z, t)∈ ℍn be the distance function in ℍn. Denote ℍ …

A new Adams' inequality involving the Bilaplacian operators and applications to some biharmonic nonlocal equation

S Aouaoui - Annali di Matematica Pura ed Applicata (1923-), 2024 - Springer
In this paper, we prove some new inequality of Adams' type for some new higher order
Sobolev space whose norm is a combination of the norms of the N 2-Bilaplacian and the p …

Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights

R Arora, J Giacomoni, T Mukherjee, K Sreenadh - Nonlinear Analysis, 2020 - Elsevier
In this work, we study the higher order Kirchhoff type Choquard equation (KC) involving a
critical exponential non-linearity and singular weights. We prove the existence of solution to …

Sharp affine and improved Moser–Trudinger–Adams type inequalities on unbounded domains in the spirit of Lions

N Lam, G Lu, H Tang - The Journal of Geometric Analysis, 2017 - Springer
The purpose of this paper is threefold. First, we prove sharp singular affine Moser–Trudinger
inequalities on both bounded and unbounded domains in R^ n R n. In particular, we will …

Existence and non-existence of maximizers for the Moser–Trudinger type inequalities under inhomogeneous constraints

N Ikoma, M Ishiwata, H Wadade - Mathematische Annalen, 2019 - Springer
In this paper, we study the existence and non-existence of maximizers for the Moser–
Trudinger type inequalities in R^ N RN of the form D_ N, α (a, b):=\sup _ u ∈ W^ 1, N (R …