EPSILON-REGULARITY FOR THE SOLUTIONS OF FREE BOUNDARY SYSTEMS

We will present some new results for a class of free boundary systems associated to shape optimization problems (spectral and integral functionals). The new main point of these results is the analysis of the regular part of the free boundary based on a linearization argument that takes care of the vectorial attitude of the problem.
This is based on joint works with D. De Silva and with F.P. Maiale and B. Velichkov.