Survey
Inserted: 7 nov 2014
Last Updated: 7 nov 2014
Year: 2014
Abstract:
In this survey we present the new techniques developed for proving existence of optimal sets when one minimizes functionals depending on the eigenvalues of the Dirichlet Laplacian with a measure constraint, the most important being:\[
\min{\left\{\lambda_k(\Omega)\;:\Omega\subset\mathbb{R}^N,\;
\Omega
=1\right\}}.
\]
In particular we sketch the main ideas of some recent works, which allow to extend the now classic result by Buttazzo and Dal Maso to $\mathbb{R}^N$.
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