The eigenvalues of the Laplacian with Dirichlet boundary condition in $$\mathbb {R}^2$$ R 2 are almost never minimized by disks

Berger, Amandine

In: Annals of Global Analysis and Geometry, 2015, vol. 47, no. 3, p. 285-304

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    Summary
    Minimization of the Dirichlet eigenvalues of the Laplacian among sets of prescribed measure is a standard problem in shape optimization. The main result of this paper is that in the Euclidean plane, apart from the first four, no Dirichlet eigenvalue can be minimized by disks or disjoint unions of disks.