Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|Number of page(s)||13|
|Published online||30 April 2021|
An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams*
Dipartimento di Matematica, Università di Pisa Largo B. Pontecorvo 5,
** Corresponding author: firstname.lastname@example.org
Accepted: 3 April 2021
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 ⊂⊂ ℝd 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 ↦ Ωt, 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 ℝd. This allows to obtain a sharp characterization of the Blaschke-Santaló diagram of torsion and eigenvalue.
Mathematics Subject Classification: 49Q10 / 49J45 / 49R05 / 35P15 / 35J25
Key words: Blaschke-Santaló diagrams / continuous Steiner symmetrization / torsional rigidity / principal eigenvalue
© EDP Sciences, SMAI 2021
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