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The eigenvalue problem with conductivity boundary conditions

Bucur D., Durus I., Oudet E.

Control and Cybernetics

2008

Vol. 37, no 4

811-829

In this paper we study isoperimetric inequalities for the eigenvalues of the Laplace operator with constant and locally constant boundary conditions. Existence and stability results are presented in the of the gamma and weak gamma convergencies, together with identification of optimal sets by analytical and numerical methods.

How to prove existence in shape optimization

Bucur D.

Control and Cybernetics

2005

Vol. 34, no 1

103-116

This paper deals with the existence question in optimal design. We present, a general variational technique for proving existence, and give several examples concerning functionals of eigenvalues and of energy type. In particular, we show how the isoperi-metric problem for the Dirichlet eigenvalues of an elliptic operator of general order fits into this frame.