On the boundary of the attainable set of the dirichlet spectrum - Brasco, Lorenzo; Nitsch, Carlo; Pratelli, Aldo (Zeitschrift für Angewandte Mathematik und Physik, 2013)
Denoting by the set of the pairs for all the open sets with unit measure, and by the union of two disjoint balls of half measure, we give an elementary proof of the fact that has horizontal tangent at its lowest point .
Keywords: Dirichlet-Laplacian spectrum; Shape optimization