Published Paper

Inserted: 7 sep 2020
Last Updated: 12 oct 2021

Journal: Calc. Var. PDE
Year: 2020
Notes:

32 pages

Abstract:

We study a spectral optimization problem made as the sum of the first Dirichlet Laplacian eigenvalue, and the relative strength of a Riesz-type interaction functional. We show that when the Riesz repulsion strength is below a critical value, existence of minimizers occurs and they are $C^{1,\alpha}-$regular. This allows to show by means of an expansion analysis that the ball is a rigid minimizer as the Riesz repulsion is small enough. Eventually we show that for certain regimes of the Riesz repulsion, regular minimizers do not exist.

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