Lorenzo Lamberti on “Regularity results for an Optimal Design Problem with lower order terms”

We study the regularity of the interface for optimal energy
configurations of functionals involving bulk energies with an
additional perimeter penalization of the interface. It is allowed
the dependence on (x,u) for the bulk energy. For a minimal
configuration (u,A), the Hölder continuity of u is well known.
We give an estimate for the singular set of the boundary of A,
showing that its Hausdorff dimension is strictly smaller than

n-1.

This talk is based on a joint work with Luca Esposito.