Author

Yang-Yang Zhang

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Preprint Aug 2026

$\Gamma$-Convergence of Weak-Type Nonlocal Functionals on Bounded Domains

Let $N\ge1$, $p\in[1,\infty)$, $\gamma\in(0,\infty)$, and $\Omega\subset\mathbb R^N$ be a bounded open interval when $N=1$ or a bounded Lipschitz domain when $N\ge2$. For any $\lambda\in(0,\infty)$ and any measurable function $u$, consider the weak-type nonlocal functional \begin{align*} G_{\lambda,p,\gamma}(u;\Omega)...

Xiao-Sheng Lin, Da-Chun Yang, Sibei Yang et al. · 2 citations · ⚡2

Preprint Aug 2026

Capacitary-Distance Hardy Inequality

Let $n\ge3$, $\Omega\subset\mathbb R^n$ be an open set, $F:=\mathbb R^n\setminus\Omega$, and $\alpha\in(0,\infty)$. For any $x\in\Omega$, we define the capacitary distance \begin{align*} d_\alpha(x) := \inf\left\{ r>0: \operatorname{cap}(\overline{F\cap B(x,r)}) \ge \alpha\operatorname{cap}(B(\mathbf0,r)) \right\}. \en...

Yi-Qun Chen, Jie Xiao, Dachun Yang et al. · 0 citations