37 citations · 115 across the 22 of their papers we have counts for
6 papers · 1 filter
On the boundary of the attainable set of the Dirichlet spectrum
Lorenzo Brasco, Carlo Nitsch, Aldo Pratelli
Denoting by the set of the pairs for all the open sets with unit measure, and by the union of two di…
Existence of minimizers for spectral problems
Dario Mazzoleni, Aldo Pratelli
In this paper we show that any increasing functional of the first k eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of R^N of unit measure.…
Existence of isoperimetric regions in with density
Frank Morgan, Aldo Pratelli
We prove the existence of isoperimetric regions in with density under various hypotheses on the growth of the density. Along the way we prove results on the boundedness of i…
A planar bi-Lipschitz extension Theorem
Sara Daneri, Aldo Pratelli
We prove that, given a planar bi-Lipschitz homeomorphism defined on the boundary of the unit square, it is possible to extend it to a function of the whole square, in such…
Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms
Sara Daneri, Aldo Pratelli
We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the norm, together with its inverse, with an orientation-preserving homeomo…
Quantitative stability in the isodiametric inequality via the isoperimetric inequality
Francesco Maggi, Marcello Ponsiglione, Aldo Pratelli
The isodiametric inequality is derived from the isoperimetric inequality trough a variational principle, establishing that balls maximize the perimeter among convex sets with fixed…