|Location:||MSRI: Baker Board Room|
- prove the existence of an optimal shape without imposing any a priori smoothness constraint. A relaxation phenomenon may be observed, the solution being a measure or a quasi-open set.
- study the regularity of the optimal shape. This is a difficult problem, but sometimes mild regularity may be enough to extract optimality conditions.
- write optimality conditions and get qualitative information on the optimal shape.
I will give some recent results involving the eigenvalues of the Laplace operator with Robin boundary conditions and I will discuss both the optimal design and the free boundary points of view.