Calculus of Variations and Geometric Measure Theory

D. Bucur - D. Mazzoleni

A surgery result for the spectrum of the Dirichlet Laplacian

created by mazzoleni on 20 Oct 2014
modified on 05 Aug 2016


Published Paper

Inserted: 20 oct 2014
Last Updated: 5 aug 2016

Journal: SIAM J. Math. Anal.
Volume: 47
Number: 6
Pages: 4451-4466
Year: 2015
Doi: 10.1137/140992448


In this paper we give a method to geometrically modify an open set such that the first $k$ eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure remains constant, and both perimeter and diameter decrease below a certain threshold. The key point of the analysis relies on the properties of the shape subsolutions for the torsion energy.