Special Session 141: New trends and methods for differential problems

Spectral clusters
Giorgio Saracco
Universita` di Ferrara
Italy
Co-Author(s):    Giorgio Stefani
Abstract:
Given any open, bounded set $\Omega$, we consider suitable combinations, via a reference function $\Phi$, of the first $p$-eigenvalue of the Dirichlet Laplacian of partitions of $\Omega$. We give two different formulations of the problem, one geometrical and one functional. We prove relations among the two formulations, existence and regularity of optimal partitions, convergence, and stability with respect to $p$ and to $\Phi$. Based on a joint work with G. Stefani (Padova).