In this paper the author studies the isoperimetric problem in \ren 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.
@article{arxiv.1706.09619,
title = {On the isoperimetric problem with perimeter density r^p},
author = {Gyula Csato},
journal= {arXiv preprint arXiv:1706.09619},
year = {2017}
}