We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Dirichlet Laplacian 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. Then we prove, by means of an expansion analysis, that the ball is a rigid minimizer when the Riesz repulsion is small enough. Eventually we show that for certain regimes of the Riesz repulsion, regular minimizers do not exist.
Mazzoleni, D., Ruffini, B. (2021). A spectral shape optimization problem with a nonlocal competing term. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 60(3), 1-46 [10.1007/s00526-021-01972-0].
A spectral shape optimization problem with a nonlocal competing term
Mazzoleni, D;Ruffini, B
2021
Abstract
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Dirichlet Laplacian 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. Then we prove, by means of an expansion analysis, that the ball is a rigid minimizer when the Riesz repulsion is small enough. Eventually we show that for certain regimes of the Riesz repulsion, regular minimizers do not exist.| File | Dimensione | Formato | |
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