A review on large k minimal spectral k-partitions and Pleijel’s Theorem.

We would like to analyze the relations between the nodal domains of the eigenfunctions of the Dirichlet Laplacians and the partitions by k open sets D i which are minimal in the

We would like to analyze the relations between the nodal domains of the eigenfunctions of the Dirichlet Laplacians and the partitions by k open sets D i which are minimal in the

We would like to analyze the relations between the nodal domains of the eigenfunctions of the Dirichlet Laplacians and the partitions by k open sets D i which are minimal in the

We would like to analyze the relations between the nodal domains of the eigenfunctions of the Dirichlet Laplacians and the partitions by k open sets D i which are minimal in the

S´ark¨ozy, “On the number of partitions of n without a given subsum II,” in Analytic Number Theory (B. Szalay, “On some problems

In particular, we would like to determine in which cases this minimal partition is actually the family of the nodal domains of a given eigenfunction of the two-dimensional

The main results concern the existence and regularity of the minimal partitions and the characterization of the minimal partitions associated with nodal sets as the nodal domains

Computations are made in the latter case to provide candidates for minimal 3-partitions, using symmetry to reduce the analysis to the determination of the nodal sets of the