8 papers · 1 filter
Small-energy regularity for stationary weak solutions of the Liouville equation
Haotong Fu, Kelei Wang, Wei Wang +1
We establish small-energy regularity for stationary weak solutions of the Liouville equation in every dimension. It solves a problem left open in Da Lio [Commun. Partia…
Boundary asymptotics for two-dimensional vectorial Allen-Cahn systems
Zhiyuan Dai, Haotong Fu, Huaijie Wang +1
We study asymptotic properties of critical points of the two-dimensional vectorial Allen-Cahn energy with finitely many non-degenerate wells, subject to a homogeneous Neumann bound…
Boundary regularity for Oseen-Frank minimizers with arbitrary positive splay, twist, and bend constants
Zhiyuan Dai, Haotong Fu, Huaijie Wang +1
Let be a smooth bounded domain and let be smooth. We prove that any global minimizer of the Oseen--Frank energy subject to the str…
Smooth Convergence of Landau-de Gennes Minimizers in the Lyuksyutov Regime
Haotong Fu, Huaijie Wang, Wei Wang
In this paper, we analyze global minimizers of the Landau--de Gennes functional in 3-dimensional domains in the Lyuksyutov regime. We prove smooth convergence to an -…
On the absence of point defects in biaxial Landau--de Gennes models
Haotong Fu, Huaijie Wang, Wei Wang +1
We study local minimizers of a sextic-potential Landau--de Gennes energy for nematic liquid crystals in the small-elastic-constant limit. Under the uniform energy and bo…
Singular Limits for Three-Dimensional Global Minimizers of Ginzburg--Landau-Type Functionals: Uniform Estimates and Singular Sets
Giacomo Canevari, Haotong Fu, Wei Wang
We study the asymptotic behavior of global minimizers of a Ginzburg--Landau-type functional with general compact vacuum manifold on bounded domains in ,…
A Note on an Approximate Fixed Point Theorem for Maps
Haotong Fu, Wei Wang
We prove an approximate fixed point theorem for maps of vanishing mean oscillation from the unit ball to itself. This gives a short proof of the Open Problem 5.10 of Brezis [Rend.…
Asymptotics of Minimizers for Ginzburg--Landau-type Functionals in High Dimensions
Giacomo Canevari, Haotong Fu, Wei Wang
We investigate local minimizers of Ginzburg--Landau-type functionals in dimension that satisfy logarithmic energy bounds, assuming the potential has a vacuum manifold wit…