Calculus of Variations and Geometric Measure Theory

E. Cinti - A. Pratelli

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

created by cinti on 23 Mar 2015
modified by pratelli on 17 Dec 2019


Published Paper

Inserted: 23 mar 2015
Last Updated: 17 dec 2019

Journal: Math. Ann.
Year: 2017


We consider the isoperimetric problem in $\mathbb R^n$ with density for the planar case $n=2$. We show that, if the density is ${\rm C}^{0,\alpha}$, then the boundary of any isoperimetric is of class ${\rm C}^{1,\frac \alpha{3-2\alpha}}$. This improves the previously known regularity.