Calculus of Variations and Geometric Measure Theory

Z. Belhachmi - D. Bucur - G. Buttazzo - J. M. Sac-Epée

Shape optimization problems for eigenvalues of elliptic operators

created by buttazzo on 27 May 2005



Inserted: 27 may 2005

Year: 2005


We consider a general formulation for optimization problems involving the eigenvalues of the Laplace operator. Both the cases of Dirichlet and Neumann conditions on the free boundary are studied. We list several results concerning the existence of optimal domains, together with some conjectures and open problems. The last section contains some numerical computations.

Keywords: shape optimization, eigenvalues, Laplace operator, Finite elements method