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• W2182366276 abstract "We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet–Laplacian among open sets of RN of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure." @default.
• W2182366276 created "2016-06-24" @default.
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• W2182366276 date "2017-04-07" @default.
• W2182366276 modified "2023-10-15" @default.
• W2182366276 title "Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets" @default.
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• W2182366276 doi "https://doi.org/10.1051/cocv/2016017" @default.
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