Nodal minimal partitions in dimension $3$
Bernard Helffer Thomas Hoffmann-Ostenhof Susanna Terracini
In continuation of [20], we analyze the properties of spectral minimal $k$-partitions of an open set $\Omega$ in $\mathbb R^3$ which are nodal, i.e. produced by the nodal domains of an eigenfunction of the Dirichlet Laplacian in $\Omega$. 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.
keywords: Optimal partitions; Eigenvalues; Nodal domains; Courant nodal Theorem; Spectral minimal partitions.

Year of publication

Related Authors

Related Keywords

[Back to Top]