  In this article we are interested in studying partitions of the square, the
disk and the equilateral triangle which minimize a p-norm of eigenvalues of the
Dirichlet-Laplace operator. The extremal case of the infinity norm, where we
minimize the largest fundamental eigenvalue of each cell, is one of our main
interests. We propose three numerical algorithms which approximate the optimal
configurations and we obtain tight upper bounds for the energy, which are
better than the ones given by theoretical results. A thorough comparison of the
results obtained by the three methods is given. We also investigate the
behavior of the minimal partitions with respect to p. This allows us to see
when partitions minimizing the 1-norm and the infinity-norm are different.
