Abstract
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.
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Cited by
1 articles.
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