Journal of Convex Analysis 30 (2023), No. 2, 615--626
Copyright Heldermann Verlag 2023
On the Continuity of the Continuous Steiner Symmetrization
Dip. di Matematica, UniversitÓ di Pisa, Italy
Starting from the Brock's construction of Continuous Steiner Symmetrization of sets, the problem of modifying continuously a given domain up to obtain a ball, preserving its measure and with decreasing first eigenvalue of the Laplace operator, is considered. For a large class of cases it is shown this is possible, while the general question remains still open.
Keywords: Steiner symmetrization, shape optimization, torsional rigidity, first eigenvalue, Gamma-convergence.
MSC: 49Q10, 35P15, 49R50, 49J45, 49R05.
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