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- W1587982819 abstract "We address the question of determining the eigenvalues $${lambda_{n}}$$ (listed in nondecreasing order, with multiplicities) for which Courant’s nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with $${n}$$ nodal domains (Courant-sharp eigenvalues). Following ideas going back to Pleijel (1956), we prove that the only Courant-sharp eigenvalues of the flat equilateral torus are the first and second, and that the only Courant-sharp Dirichlet eigenvalues of the equilateral triangle are the first, second, and fourth eigenvalues. In the last section we sketch similar results for the right-angled isosceles triangle and for the hemiequilateral triangle." @default.
- W1587982819 created "2016-06-24" @default.
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- W1587982819 date "2016-02-09" @default.
- W1587982819 modified "2023-10-01" @default.
- W1587982819 title "Courant-Sharp Eigenvalues for the Equilateral Torus, and for the Equilateral Triangle" @default.
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- W1587982819 doi "https://doi.org/10.1007/s11005-016-0819-9" @default.
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