In this talk,we analyze the connections between the nodal domains of the eigenfunctions of the Dirichlet-Laplacian and the partitions of the domain by k open sets Di which are minimal in the sense that the maximum over the Di's of the groundstate energy of the Dirichlet realization of the Laplacian is minimal. Instead of considering the maximum among the first eigenvalues, we can also consider the p-norm of the vector composed by the first eigenvalues of each subdomain.