# On the isoperimetric problem with perimeter density r^p

created by csato on 12 Nov 2021

[BibTeX]

preprint

Inserted: 12 nov 2021

Year: 2017

ArXiv: 1706.09619 PDF

Abstract:

In this paper the author studies the isoperimetric problem in $\re^n$ 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 $0\leq p\leq 1$ and deal with the case $-\infty<p<-1$ (with the additional assumption $0\in\Omega$). In the case $n\geq 3$ we deal mainly with the case $-\infty<p<0,$ showing among others that the results in $2$ dimensions do not generalize for the range $-n+1<p<0.$

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