45 citations · 187 across the 43 of their papers we have counts for
13 papers · 1 filter
Sharp Caffarelli-Kohn-Nirenberg inequalities on Riemannian manifolds: the influence of curvature
Van Hoang Nguyen
We first establish a family of sharp Caffarelli-Kohn-Nirenberg type inequalities on the Euclidean spaces and then extend them to the setting of Cartan-Hadamard manifolds with the s…
Sharp Hardy and Rellich type inequalities on Cartan--Hadamard manifolds and their improvements
Van Hoang Nguyen
In this paper, we prove several new Hardy type inequalities (such as the weighted Hardy inequality, weighted Rellich inequality, critical Hardy inequality and critical Rellich ineq…
Improved Moser-Trudinger type inequalities in the hyperbolic space
Van Hoang Nguyen
We establish an improved version of the Moser-Trudinger inequality in the hyperbolic space , . Namely, we prove the following result: for any $0 \leq λ< \left…
The sharp higher order Hardy--Rellich type inequalities on the homogeneous groups
Van Hoang Nguyen
We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequaliti…
Improved Moser--Trudinger inequality for functions with mean value zero in and its extremal functions
Van Hoang Nguyen
Let be a bounded smooth domain in , be the Sobolev space on , and be the first nonzero…
A pointwise inequality for a biharmonic equation with negative exponent and related problems
Quôc Anh Ngô, Van Hoang Nguyen, Quoc Hung Phan
Inspired by a recent pointwise differential inequality for positive bounded solutions of the fourth-order Hénon equation in with …
Extremal functions for the sharp Moser--Trudinger type inequalities in whole space
Van Hoang Nguyen
This paper is devoted to study the sharp Moser-Trudinger type inequalities in whole space , in more general case. We first compute explicitly the \emph{norm…
On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem
Van Hoang Nguyen, Futoshi Takahashi
In this paper, we establish a weighted Trudinger-Moser type inequality with the full Sobolev norm constraint on the whole Euclidean space. Main tool is the singular Trudinger-Moser…
Maximizers for the variational problems associated with Sobolev type inequalities under constraints
Van Hoang Nguyen
We propose a new approach to study the existence and non-existence of maximizers for the variational problems associated with Sobolev type inequalities both in the subcritical case…
An improved Moser-Trudinger inequality involving the first non-zero Neumann eigenvalue with mean value zero in
Quôc-Anh Ngô, Van Hoang Nguyen
Let be a smooth bounded domain in and the first non-zero Neumann eigenvalue of the operator on . In this paper, for any $γ\in [0, λ^{\…
The sharp Gagliardo--Nirenberg--Sobolev inequality in quantitative form
Van Hoang Nguyen
Using a dimension reduction argument and a stability version of the weighted Sobolev inequality on half space recently proved by Seuffert, we establish, in this paper, some stabili…
Extremal functions for the Moser--Trudinger inequality of Adimurthi--Druet type in
Van Hoang Nguyen
We study the existence and nonexistence of maximizers for variational problem concerning to the Moser--Trudinger inequality of Adimurthi--Druet type in \[ MT…
A sharp Adams inequality in dimension four and its extremal functions
Van Hoang Nguyen
Let be a smooth oriented bounded domain in , be the Sobolev space, and be the first eigenvalue…