In this paper the author studies the isoperimetric problem in ${\mathbb{R}}^n$ with perimeter density $|x|^p$ and volume density 1. We settle completely the case $n = 2$ , completing a previous work by the author: we characterize the case of equality if $0≤p≤1$ and deal with the case $-∞<p<-1$ (with the additional assumption $0∈Ω$ ). In the case $n≥3$ we deal mainly with the case $-∞<p<0$ , showing among others that the results in 2 dimensions do not generalize for the range $-n+1<p<0.$
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