Dichotomy of global capacity density
Dichotomy of global capacity density
Let $1<p<\infty$ and let $d\mu (x)=w(x)dx$ be a $p$-admissible weight in $\mathbb {R}^n$, $n\ge 2$. By $\mathrm {Cap}_{p,\mu }(E,D)$ we denote the variational $(p,\mu )$-capacity of condenser $(E,D)$. We show a dichotomy of the global density with respect to $\mathrm {Cap}_{p,\mu }$. One of our results is as follows: Let …