Buttazzo, G. ; Casas, E. ; de Teresa, L. ; Glowinski, R. ; Leugering, G. ; Trélat, E. ; Zhang, X.(éd.)
In this paper we consider the so-called procedure of Continuous Steiner Symmetrization, introduced by Brock in [F. Brock, Math. Nachr. 172 (1995) 25–48 and F. Brock, Proc. Indian Acad. Sci. 110 (2000) 157–204]. It transforms every open set Ω ⊂⊂ ℝ$$ into the ball keeping the volume fixed and letting the first eigenvalue and the torsional rigidity respectively decrease and increase. While this does not provide, in general, a γ-continuous map t ↦ Ω$$, it can be slightly modified so to obtain the γ-continuity for a γ-dense class of domains Ω, namely, the class of polyhedral sets in ℝ$$. This allows to obtain a sharp characterization of the Blaschke-Santaló diagram of torsion and eigenvalue.
Keywords: Blaschke-Santaló diagrams, continuous Steiner symmetrization, torsional rigidity, principal eigenvalue
@article{COCV_2021__27_1_A38_0,
author = {Buttazzo, Giuseppe and Pratelli, Aldo},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {An application of the continuous {Steiner} symmetrization to {Blaschke-Santal\'o} diagrams},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021038},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021038/}
}
TY - JOUR AU - Buttazzo, Giuseppe AU - Pratelli, Aldo ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021038/ DO - 10.1051/cocv/2021038 LA - en ID - COCV_2021__27_1_A38_0 ER -
%0 Journal Article %A Buttazzo, Giuseppe %A Pratelli, Aldo %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021038/ %R 10.1051/cocv/2021038 %G en %F COCV_2021__27_1_A38_0
Buttazzo, Giuseppe; Pratelli, Aldo. An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 36. doi: 10.1051/cocv/2021038
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Dedicated to Enrique Zuazua for his 60th birthday.
