Optimal regularity for isoperimetric sets with density

In this talk, I will present a recent result which establishes optimal regularity for isoperimetric sets with densities, under mild H\¨older regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to reach the optimal regularity class $C^{1, \frac{α}{2−α}}$ in any dimension. This is a joint work with L. Beck and C. Seis.