Inserted: 16 feb 2015
Last Updated: 1 sep 2017
Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
The aim of this survey is to give a precise idea of the recent results on existence of isoperimetric sets in $\mathbb R^N$ with density. We will mainly focus on the overall ideas, leaving away some technical details of the proofs, which can be found in the cited papers. No previous knowledge on the subject is assumed from the reader.\par
This survey originates from a talk of the author at the conference ``New Trends in Nonlinear PDE's'' held at the Accademia dei Lincei on November 26th, 2013.