Calculus of Variations and Geometric Measure Theory

D. Bucur - I. FragalĂ 

Symmetry results for variational energies on convex polygons

created by bucur on 29 Aug 2020


Submitted Paper

Inserted: 29 aug 2020
Last Updated: 29 aug 2020

Year: 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.