  We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the
second author and Nikolai Nadirashvili of a bounded domain in R2 for which the
second eigenvalue of the Dirichlet Laplacian has multiplicity three. We also
analyze carefully the first eigenvalues of the Laplacian in the case of the
disk with two symmetric cracks placed on a smaller concentric disk in function
of their size.
