Shape optimization problems for eigenvalues of elliptic operators
Zakaria Belhachmi, Dorin Bucur, Giuseppe Buttazzo, Jean-Marc Sac-Épée · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2006
Abstract We consider a general formulation for shape optimization problems involving the eigenvalues of the Laplace operator. Both the cases of Dirichlet and Neumann conditions on the free boundary are studied. We survey the most recent results concerning the existence of optimal domains, and list some conjectures and open problems. Some open problems are supported by efficient numerical computations.