Author

Hui Yang

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Preprint Sep 2026

The direct moving plane method for weak solutions of the fractional $p$-Laplacian

In this paper, we develop the method of moving planes entirely in the weak formulation for the fractional $p$-Laplacian in the singular range $1<p\leq2$. We first establish a small region principle for antisymmetric functions and apply it to prove radial symmetry and monotonicity of nonnegative weak solutions of fracti...

Meiqing Xu, Hui Yang · 0 citations

Preprint Sep 2026

Symmetry, monotonicity, and asymptotics of singular solutions to semilinear elliptic equations

In this paper, we study singular positive solutions to the semilinear elliptic equation $$ - \Delta u = f(u) ~~~~~~ \textmd{in} ~ \Omega \setminus \Gamma, $$ where $\Omega \subset \R^n$ is a bounded or unbounded domain, and $\Gamma \subset \Omega$ is a singular closed set with zero Newtonian capacity. When $\Omega = \R...

Xu-Sheng Du, Hui Yang · 0 citations

Preprint Aug 2026

On the structure of isolated singularities for semilinear elliptic equations

In this paper, we study isolated singularities of the following semilinear elliptic equation $-\Delta u+\frac12 x\cdot \nabla u+\frac{1}{q-1}u-u^q=0$ in $\Omega \setminus \{0\}$, where $n\ge 3$, $\Omega \subset \mathbb{R}^n$ is a domain, $0 \in \Omega$ and $q>1$. This equation arises in the study of blow-up profiles of...

Meiqing Xu, Hui Yang · 0 citations