# Symmetry results for variational energies on convex polygons

created by bucur on 29 Aug 2020

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Submitted Paper

Inserted: 29 aug 2020
Last Updated: 29 aug 2020

Year: 2020

Abstract:

We prove that, in the class of convex polygons with a given number of sides, the regular $n$-gon is optimal for some shape optimization problems involving the torsional rigidity, the principal frequency of the Laplacian, or the logarithmic capacity.