5 papers · 1 filter
The direct moving plane method for weak solutions of the fractional -Laplacian
Meiqing Xu, Hui Yang
In this paper, we develop the method of moving planes entirely in the weak formulation for the fractional -Laplacian in the singular range . We first establish a small…
On the structure of isolated singularities for semilinear elliptic equations
Meiqing Xu, Hui Yang
In this paper, we study isolated singularities of the following semilinear elliptic equation in , where $n\ge 3…
Liouville theorems for conformal -curvature equations
Meiqing Xu, Hui Yang
In this paper, we study the non-existence of positive solutions for the following conformal -curvature equation \begin{equation*} (-Δ)^σu = K(x) u^{\frac{n+2σ}{n-2σ}} \quad \tex…
On isolated singularities of the conformal Gaussian curvature equation and -curvature equation
Hui Yang, Ronghao Yang
In this paper, we study the isolated singularities of the conformal Gaussian curvature equation \[ -Δu = K(x) e^{u} \quad ~ in ~ B_{1} \setminus \{ 0 \}, \] where $B_1 \setminus \{…
The direct moving sphere for fractional Laplace equation
Congming Li, Meiqing Xu, Hui Yang +1
This paper works on the direct method of moving spheres and establishes a Liouville-type theorem for the fractional elliptic equation \[ (-Δ)^{α/2} u =f(u) ~~~~~~ \text{in } \mathb…