A spectral shape optimization problem with a nonlocal competing term
2021 ◽
Vol 60
(3)
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Keyword(s):
AbstractWe 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.
2015 ◽
Vol 145
(6)
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pp. 1145-1151
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2018 ◽
Vol 291
(4)
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pp. 632-651
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2016 ◽
Vol 113
(3)
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pp. 387-417
2006 ◽
Vol 5
(4)
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pp. 675-690
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2015 ◽
Vol 373
(2050)
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pp. 20140273
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