# Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions

@article{Privat2018SpectralSO,
title={Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions},
author={Yannick Privat and Emmanuel Tr{\'e}lat and Enrique Zuazua},
journal={Calculus of Variations and Partial Differential Equations},
year={2018},
volume={58},
pages={1-45}
}
We consider a spectral optimal design problem involving the Neumann traces of the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset $$\Omega$$Ω of . The cost functional measures the amount of energy that Dirichlet eigenfunctions concentrate on the boundary and that can be recovered with a bounded density function. We first prove that, assuming a $$L^1$$L1 constraint on densities, the so-called Rellich functions maximize this functional. Motivated by several issues in shape… CONTINUE READING
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