Premium
Shape optimization problems for eigenvalues of elliptic operators
Author(s) -
Belhachmi Z.,
Bucur D.,
Buttazzo G.,
SacEpée J.M.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510259
Subject(s) - eigenvalues and eigenvectors , elliptic operator , mathematics , neumann boundary condition , operator (biology) , boundary value problem , computation , laplace operator , dirichlet distribution , dirichlet eigenvalue , dirichlet boundary condition , mathematical analysis , algorithm , dirichlet's principle , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
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.