In:
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, Vol. 27 ( 2021), p. 36-
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 ⊂⊂ ℝ d 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 t , 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 d . This allows to obtain a sharp characterization of the Blaschke-Santaló diagram of torsion and eigenvalue.
Type of Medium:
Online Resource
ISSN:
1292-8119
,
1262-3377
DOI:
10.1051/cocv/2021038
Language:
English
Publisher:
EDP Sciences
Publication Date:
2021
detail.hit.zdb_id:
2032256-2
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