Luc Nguyen

activity

20092026

most citedStability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals

78 citations · 449 across the 34 of their papers we have counts for

collaborators

38 papers

math.AP2026

Two-bump axisymmetric solutions of the Nirenberg problem

Yanyan Li, Luc Nguyen, Bo Wang

In this paper, we revisit the axisymmetric Nirenberg problem for certain prescribed scalar curvature functions whose critical points include the north and south poles and whose ord…

math.AP2026

The Ginzburg-Landau system with general potential: maximum principle and gradient estimates

Radu Ignat, Luc Nguyen, Valeriy Slastikov +1

We study critical points of the Ginzburg-Landau energy functional $$\mathcal{F}_\varepsilon[u] = \int_Ω\Big[ \frac{1}{2}|\nabla u|^2 + \frac{1}{2\varepsilon^2} W(1 - |u|^2)\Big]\,d…

math.AP2022

Mean oscillation gradient estimates for elliptic systems in divergence form with VMO coefficients

Luc Nguyen

We consider gradient estimates for $H^{1}$ solutions of linear elliptic systems in divergence form $\partial_{α} (A_{ij}^{α β} \partial_{β} u^{j}) = 0$ . It is known that the Dini continuity o…

math.AP2022★ 9 cited

Regularity of viscosity solutions of the $σ_{k}$ -Loewner-Nirenberg problem

YanYan Li, Luc Nguyen, Jingang Xiong

We study the regularity of the viscosity solution $u$ of the $σ_{k}$ -Loewner-Nirenberg problem on a bounded smooth domain $Ω \subset R^{n}$ for $k \geq 2$ . It was known that $u…

math.AP2021

Local minimality of $R^{N}$ -valued and $S^{N}$ -valued Ginzburg-Landau vortex solutions in the unit ball $B^{N}$

Radu Ignat, Luc Nguyen

We study the existence, uniqueness and minimality of critical points of the form $m_{ε, η} (x) = (f_{ε, η} (∣ x ∣) \frac{x}{∣ x ∣}, g_{ε, η} (∣ x ∣))$ of the funct…

math.AP2021

The axisymmetric $σ_{k}$ -Nirenberg problem

Yanyan Li, Luc Nguyen, Bo Wang

We study the problem of prescribing $σ_{k}$ -curvature for a conformal metric on the standard sphere $S^{n}$ with $2 \leq k < n /2$ and $n \geq 5$ in axisymmetry. Compactness, n…

Two-bump axisymmetric solutions of the Nirenberg problem

The Ginzburg-Landau system with general potential: maximum principle and gradient estimates

Mean oscillation gradient estimates for elliptic systems in divergence form with VMO coefficients

Regularity of viscosity solutions of the σk​-Loewner-Nirenberg problem

Local minimality of RN-valued and SN-valued Ginzburg-Landau vortex solutions in the unit ball BN

The axisymmetric σk​-Nirenberg problem

Regularity of viscosity solutions of the $σ_{k}$ -Loewner-Nirenberg problem

Local minimality of $R^{N}$ -valued and $S^{N}$ -valued Ginzburg-Landau vortex solutions in the unit ball $B^{N}$

The axisymmetric $σ_{k}$ -Nirenberg problem