Symmetry results for variational energies on convex polygons
Dorin Bucur, Ilaria Fragalà · ESAIM Control Optimisation and Calculus of Variations · 2020
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.