| Issue |
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 16 | |
| DOI | https://doi.org/10.1051/cocv/2020083 | |
| Published online | 20 January 2021 | |
Symmetry results for variational energies on convex polygons
1
Université Savoie Mont Blanc, Laboratoire de Mathématiques, CNRS UMR 5127, Campus Scientifique,
73376
Le-Bourget-Du-Lac, France.
2
Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci,
32 20133
Milano, Italy.
* Corresponding author: dorin.bucur@univ-savoie.fr
Received:
27
August
2020
Accepted:
27
November
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.
Mathematics Subject Classification: 49Q10 / 35A15 / 52B60 / 52A40
Key words: Shape optimization / polygons / Polya’s conjecture / eigenvalues / torsional rigidity
© EDP Sciences, SMAI 2021
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