Volume 27, 2021
Special issue in the honor of Enrique Zuazua's 60th birthday
|Number of page(s)||16|
|Published online||20 January 2021|
Symmetry results for variational energies on convex polygons
Université Savoie Mont Blanc, Laboratoire de Mathématiques, CNRS UMR 5127, Campus Scientifique,
2 Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci, 32 20133 Milano, Italy.
* Corresponding author: email@example.com
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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