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- W2262378339 abstract "In this paper, we determine, in the case of the Laplacian on the flat three-dimensional torus $(mathbb{R}/mathbb{Z})^3$, all the eigenvalues having an eigenfunction which satisfies the Courant nodal domains theorem with equality (Courant-sharp situation). Following the strategy of A. Pleijel (1956), the proof is a combination of an explicit lower bound of the counting function and a Faber-Krahn-type inequality for domains on the torus, deduced as, in the work of P. Berard and D. Meyer (1982), from an isoperimetric inequality. This inequality relies on the work of L. Hauswirth, J. Perez, P. Romon, and A. Ros (2004) on the periodic isoperimetric problem." @default.
- W2262378339 created "2016-06-24" @default.
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- W2262378339 date "2015-11-13" @default.
- W2262378339 modified "2023-10-01" @default.
- W2262378339 title "Courant-sharp eigenvalues of the three-dimensional square torus" @default.
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