On existence of minimizers for weighted $L^p$-Hardy inequalities on $C^{1,\gamma }$-domains with compact boundary

Ujjal Das, Yehuda Pinchover, Baptiste Devyver

Let $p\in (1,\infty )$, $\alpha \in \mathbb{R}$, and $\Omega ⊊{\mathbb{R}}^N$ be a $C^{1,\gamma }$-domain with a compact boundary $\partial \Omega$, where $\gamma \in (0,1]$. Denote by ${\delta }_{\Omega }(x)$ the dis…