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.
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DOI : 10.1051/cocv/2020083
Keywords: Shape optimization, polygons, Polya’s conjecture, eigenvalues, torsional rigidity
@article{COCV_2021__27_1_A5_0,
author = {Bucur, Dorin and Fragal\`a, Ilaria},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {Symmetry results for variational energies on convex polygons},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2020083},
mrnumber = {4201974},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2020083/}
}
TY - JOUR AU - Bucur, Dorin AU - Fragalà, Ilaria ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - Symmetry results for variational energies on convex polygons JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2020083/ DO - 10.1051/cocv/2020083 LA - en ID - COCV_2021__27_1_A5_0 ER -
%0 Journal Article %A Bucur, Dorin %A Fragalà, Ilaria %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T Symmetry results for variational energies on convex polygons %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2020083/ %R 10.1051/cocv/2020083 %G en %F COCV_2021__27_1_A5_0
Bucur, Dorin; Fragalà, Ilaria. Symmetry results for variational energies on convex polygons. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 3. doi: 10.1051/cocv/2020083
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