Regularity of the free boundary for the two-phase Bernoulli problem.

I will illustrate a recent result obtained in collaboration with B. Velichkov and L. Spolaor concerning the regularity of the free boundaries in the two phase Bernoulli problems. The new point is the analysis of the free boundary close to branch points, where we show that it is given by the union of two C^1 graphs. This complete the analysis started by Alt Caffarelli Friedman in the 80’s.