45 citations · 187 across the 43 of their papers we have counts for
49 papers
A Fourier approach to the sharp stability of Heisenberg Uncertainty Principles of higher and fractional orders: a new perspective
Anh Do, Nguyen Lam, Guozhen Lu +1
We show that, on the Fourier side, the sharp second order Heisenberg Uncertainty Principle (HUP) and its sharp stability for functions are nothing but the first order -Caffa…
The weighted -Caffarelli-Kohn-Nirenberg inequalities for the curl-free vector fields and second order derivatives: The sharp constants and stability estimates
Anh Tuan Duong, Van Hoang Nguyen
In this paper, we study the weighted -Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives. Firstly, we prove a family of the sharp…
Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp stability and extensions
Anh Xuan Do, Nguyen Lam, Guozhen Lu +1
We introduce a new family of weighted Gaussian -Poincaré-type inequalities with explicit sharp constants, optimizers, and corresponding sharp -gradient stability estimate…
The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle
Anh Tuan Duong, Van Hoang Nguyen
In this paper we prove a class of second order Caffarelli-Kohn-Nirenberg inequalities which contains the sharp second order uncertainty principle recently established by Cazacu, Fl…
An optimal Hardy-Littlewood-Sobolev inequality on and its consequences
Quôc Anh Ngô, Quoc-Hung Nguyen, Van Hoang Nguyen
For , , and , we establish the following optimal Hardy-Littlewood-Sobolev inequality \[ \Big| \iint_{\mathbf R^n \times \mathbf R^{n-k}} \frac{f(x) g(y)}…
Liouville type theorems for fractional elliptic problems
Anh Tuan Duong, Van Hoang Nguyen
In this paper, we establish Liouville type theorems for stable solutions on the whole space to the fractional elliptic equation where the nonlinearit…
The sharp Sobolev type inequalities in the Lorentz--Sobolev spaces in the hyperbolic spaces
Van Hoang Nguyen
Let , denote the Lorentz-Sobolev spaces of order one in the hyperbolic spaces . Our aim in this paper is three-fold. Firs…
The sharp Adams type inequalities in the hyperbolic spaces under the Lorentz-Sobolev norms
Van Hoang Nguyen
Let and , we denote by the Lorentz-Sobolev space of order in the hyperbolic space . In this paper,…
The sharp higher order Lorentz--Poincaré and Lorentz--Sobolev inequalities in the hyperbolic spaces
Van Hoang Nguyen
In this paper, we study the sharp Poincaré inequality and the Sobolev inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic spaces. These results generalize th…
A Liouville type theorem for fractional elliptic equation with exponential nonlinearity
Anh Tuan Duong, Van Hoang Nguyen
In this paper, we are concerned with stable solutions to the fractional elliptic equation $$ (-Δ)^s u=e^u\mbox{ in }\mathbb R^{N}, $$ where is the fractional Laplacian wit…
The sharp Hardy--Moser--Trudinger inequality in dimension
Van Hoang Nguyen
In this paper, we prove a Hardy--Moser--Trudinger inequality in the unit ball in which improves both the classical singular Moser--Trudinger inequality…
Supercritical Moser-Trudinger inequalities and related elliptic problems
Quôc Anh Ngô, Van Hoang Nguyen
Given , we establish the following two supercritical Moser-Trudinger inequalities \[ \sup\limits_{u \in W^{1,n}_{0,{\rm rad}}(B): \int_B |\nabla u|^n dx \leq 1} \int_B \exp\bi…
A supercritical Sobolev type inequality in higher order Sobolev spaces and related higher order elliptic problems
Quôc Anh Ngô, Van Hoang Nguyen
A Sobolev type embedding for radially symmetric functions on the unit ball in , , into the variable exponent Lebesgue space , $2^…
The Leray--Adams inequality
Van Hoang Nguyen
In this paper, we establish the following Leray--Adams type inequality on a bounded domain in containing the origin, \[ \sup_{u\in C_0^\infty(Ω), \tilde I_4[u,Ω…
Higher order Sobolev trace inequalities on balls revisited
Quôc Anh Ngô, Van Hoang Nguyen, Quoc Hung Phan
Inspired by a recent sharp Sobolev trace inequality of order four on the balls found by Ache and Chang [AC15], we propose a slightly different approach to reprove…
entropy inequalities and asymmetric covariance estimates for convex measures
Van Hoang Nguyen
In this paper, we use the semi-group method and an adaptation of the method of Hörmander to establish some entropy inequalities and asymmetric covariance estimates for th…
Sharp Gagliardo--Nirenberg trace inequalities via mass transportion method and their affine versions
Van Hoang Nguyen
Exploiting the mass transportation method, we prove a dual principle which implies directly the sharp Gagliardo-Nirenberg trace inequalities which was recently proved by Bolley et…
Second order Sobolev type inequalities in the hyperbolic spaces
Van Hoang Nguyen
We establish several Poincaré--Sobolev type inequalities for the Lapalce--Beltrami operator in the hyperbolic space with . These inequalities could be…
A complete description of the asymptotic behavior at infinity of positive radial solutions to in
Quôc Anh Ngô, Van Hoang Nguyen, Quoc Hung Phan
We consider the biharmonic equation in with . It was proved that this equation has a positive classical solution if, and only if, either…
The sharp Poincaré--Sobolev type inequalities in the hyperbolic spaces
Van Hoang Nguyen
In this note, we establish a version of the Poincaré--Sobolev inequalities in the hyperbolic spaces . The interest of this result is that it relates both the Poi…
Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space
Quôc Anh Ngô, Van Hoang Nguyen, Quoc Hung Phan +1
In this paper, we are interested in entire, non-trivial, non-negative solutions and/or entire, positive solutions to the simplest models of polyharmonic equations with power-type n…
Extremals for the Singular Moser-Trudinger Inequality via n-Harmonic Transplantation
Gyula Csato, Prosenjit Roy, Van Hoang Nguyen
The Moser-Trudinger embedding has been generalized in [Adimurthi A.; Sandeep K., A singular Moser-Trudinger embedding and its applications, \textit{NoDEA Nonlinear Differential Equ…
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…