In continuation of [20], we analyze the properties of spectral minimal k-partitions of an open set Ω in ℝ3 which are nodal, i.e. produced by the nodal domains of an eigenfunction of the Dirichlet Laplacian in Ω . We show that such a partition is necessarily a nodal partition associated with a k-th eigenfunction. Hence we have in this case equality in Courant's nodal theorem.
Helffer, B., Hoffmann Ostenhof, T., Terracini, S. (2010). Nodal minimal partitions in dimension 3. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 28(2), 617-635 [10.3934/dcds.2010.28.617].
Nodal minimal partitions in dimension 3
TERRACINI, SUSANNA
2010
Abstract
In continuation of [20], we analyze the properties of spectral minimal k-partitions of an open set Ω in ℝ3 which are nodal, i.e. produced by the nodal domains of an eigenfunction of the Dirichlet Laplacian in Ω . We show that such a partition is necessarily a nodal partition associated with a k-th eigenfunction. Hence we have in this case equality in Courant's nodal theorem.
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