4 papers · 1 filter
Mixed type boundary value problem of elliptic equation in a thin domain
Dian Hu, Genggeng Huang
In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the bou…
Classification of solutions of higher order critical Choquard equation
Genggeng Huang, Yating Niu
In this paper, we classify the solutions of the following critical Choquard equation \[ (-Δ)^{\frac{n}{2}} u(x) = \int_{\mathbb{R}^n} \frac{e^{\frac{2n- μ}{2}u(y)}}{|x-y|^μ}dy e^{\…
Uniqueness of topological solutions of self-dual Chern-Simons equation with collapsing vortices
Genggeng Huang, Chang-Shou Lin
We consider the following Chern-Simons equation, \begin{equation} \label{0.1} Δu+\frac 1{\varepsilon^2} e^u(1-e^u)=4π\sum_{i=1}^N δ_{p_i^\varepsilon},\quad \text{in}\quad Ω, \end{e…
A Liouville theorem for high order degenerate elliptic equations
Genggeng Huang, Congming Li
In this paper, we apply the moving plane method to the following high order degenerate elliptic equation,\begin{equation*} (-A)^p u=u^α\text{ in } \mathbb R^{n+1}_+,n\geq 1, \end{e…