We consider the set E of the first two eigenvalues of the Dirichlet-Laplacian in Omega, where Omega is an open set N-dimensional set, which has unit measure. We give an elementary proof that the boundary of E has horizontal tangent at its lowest point, which is attained when Omega is the disjoint union of two balls of measure one half.
On the boundary of the attainable set of the Dirichlet spectrum
Pratelli A.
2013-01-01
Abstract
We consider the set E of the first two eigenvalues of the Dirichlet-Laplacian in Omega, where Omega is an open set N-dimensional set, which has unit measure. We give an elementary proof that the boundary of E has horizontal tangent at its lowest point, which is attained when Omega is the disjoint union of two balls of measure one half.File in questo prodotto:
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