Regularity of isoperimetric sets in ${\mathbb{R}}^2$ with density

Eleonora Cinti, Aldo Pratelli

We consider the isoperimetric problem in ${\mathbb{R}}^n$ with density for the planar case $n=2$. We show that, if the density is ${\mathrm{C}}^{0,\alpha }$, then the boundary of any isoperimetr…