196 citations · 661 across the 35 of their papers we have counts for
36 papers
New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture
Xiang He, Renjin Jiang, Fanghua Lin +1
We introduce the Enhanced Neumann Pólya inequality, which is stronger than Pólya's conjecture, and verify it for many classes of domains, including strip-tiling domains, Euclidean…
Asymptotic limit for the isotropic-nematic problem with anisotropic elasticity
Fanghua Lin, Wei Wang, Zhifei Zhang
We consider the isotropic-nematic interface problem for liquid crystals based on the Landau-de Gennes model. We show that when the anisotropic elastic constant is negative, t…
Nematic liquid crystal flow with partially free boundary
Fanghua Lin, Yannick Sire, Juncheng Wei +1
We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes…
Critical Sets of Elliptic Equations with Rapidly Oscillating Coefficients in Two Dimensions
Fanghua Lin, Zhongwei Shen
In this paper we continue the study of critical sets of solutions $u_\e$ of second-order elliptic equations in divergence form with rapidly oscillating and periodic coefficients. I…
Critical Sets of Solutions of Elliptic Equations in Periodic Homogenization
Fanghua Lin, Zhongwei Shen
In this paper we study critical sets of solutions $u_\e$ of second-order elliptic equations in divergence form with rapidly oscillating and periodic coefficients. We show that the…
Riesz transform on exterior Lipschitz domains and applications
Renjin Jiang, Fanghua Lin
Let be a uniformly elliptic operator on , . Let be an exterior Lipschitz domain, and let and ${\maths…
Matrix-valued Allen-Cahn equation and the Keller-Rubinstein-Sternberg problem
Mingwen Fei, Fanghua Lin, Wei Wang +1
In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: $$\partial_t A=ΔA-\varepsilon^{-2}( A A^{\mathrm{T}}A- A)~~\text{…
Boundary Harnack Principle on Nodal Domains
Fanghua Lin, Zhengjiang Lin
We study some geometric and potential theoretic properties of nodal domains of solutions to certain uniformly elliptic equations. In particular, we establish corkscrew conditions,…
Isotropic-Nematic Phase Transition and Liquid Crystal Droplets
Fanghua Lin, Changyou Wang
Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the…
Large asymptotics for minimal partitions of the Dirichlet eigenvalue
Zhiyuan Geng, Fanghua Lin
In this paper, we study large asymptotics of the minimal -partition problem for Dirichlet eigenvalue. For any smooth domain such that , we p…
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
Fanghua Lin, Jiuyi Zhu
The aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real a…
Finite time blow-up for the nematic liquid crystal flow in dimension two
Chen-Chih Lai, Fanghua Lin, Changyou Wang +2
We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain . Given any distinct points in the…
Uniform Boundary Controllability and Homogenization of Wave Equations
Fanghua Lin, Zhongwei Shen
We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are u…
Harmonic maps in connection of phase transitions with higher dimensional potential wells
Fanghua Lin, Changyou Wang
This is in the sequel of authors' paper \cite{LPW} in which we had set up a program to verify rigorously some formal statements associated with the multiple component phase transit…
Riesz transform under perturbations via heat kernel regularity
Renjin Jiang, Fanghua Lin
Let be a complete non-compact Riemannian manifold. In this paper, we derive sufficient conditions on metric perturbation for stability of -boundedness of the Riesz transfo…
Nodal Sets and Doubling Conditions in Elliptic Homogenization
Fanghua Lin, Zhongwei Shen
This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators $\{ \mathcal{…
Superfluids Passing an Obstacle and Vortex Nucleation
Fanghua Lin, Juncheng Wei
We consider a superfluid described by the Gross-Pitaevskii equation passing an obstacle \[ε^2 Δu+ u(1-|u|^2)=0 \ \mbox{in} \ {\mathbb R}^d \backslash Ω, \ \ \frac{\partial u}{\part…
On ancient solutions of the heat equation
Fanghua Lin, Qi S. Zhang
An explicit representation formula for all positive ancient solutions of the heat equation in the Euclidean case is found. In the Riemannian case with nonnegative Ricci curvature,…
Regularity for Shape Optimizers: The Degenerate Case
Dennis Kriventsov, Fanghua Lin
We consider minimizers of \[ F(λ_1(Ω),\ldots,λ_N(Ω)) + |Ω|, \] where is a function nondecreasing in each parameter, and is the -th Dirichlet eigenvalue of . This…
On the Viscous Camassa-Holm Equations with Fractional Diffusion
Zaihui Gan, Fang-Hua Lin, Jiajun Tong
We study Cauchy problem of a class of viscous Camassa-Holm equations (or Lagrangian averaged Navier-Stokes equations) with fractional diffusion in both smooth bounded domains and i…
Solvability of the Stokes Immersed Boundary Problem in Two Dimensions
Fang-Hua Lin, Jiajun Tong
We study coupled motion of a 1-D closed elastic string immersed in a 2-D Stokes flow, known as the Stokes immersed boundary problem in two dimensions. Using the fundamental solutio…
Defects of liquid crystals with variable degree of orientation
Onur Alper, Robert Hardt, Fang-Hua Lin
We prove that the zero set of a minimizer of the modified Ericksen energy for nematic liquid crystals with variable degree of orientation consists locally of isolated points and a…
On the Two-Dimensional Muskat Problem with Monotone Large Initial Data
Fan Deng, Zhen Lei, Fanghua Lin
We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous…
Structure of Helicity and Global Solutions of Incompressible Navier-Stokes Equation
Zhen Lei, Fang-Hua Lin, Yi Zhou
In this paper we derive a new energy identity for the three-dimensional incompressible Navier-Stokes equations by a special structure of helicity. The new energy functional is crit…