*Published Paper*

**Inserted:** 23 mar 2015

**Last Updated:** 1 sep 2017

**Journal:** Math. Ann.

**Year:** 2015

**Abstract:**

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.

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