Calculus of Variations and Geometric Measure Theory

D. Mazzoleni

Boundedness of minimizers for spectral problems in $\mathbb{R}^N$

created by mazzoleni on 21 Feb 2013
modified on 07 Nov 2014



Inserted: 21 feb 2013
Last Updated: 7 nov 2014

Journal: Rend. Sem. Mat. Univ. Padova
Year: 2014


In a recent paper with Aldo Pratelli we proved that any increasing functional of the first $k$ eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of $\mathbb{R}^N$ of unit measure. In this paper it is shown that every minimizer is uniformly bounded by a constant depending only on $k,N$.