  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.
