Journal of Convex Analysis 30 (2023), No. 2, 615--626
Copyright Heldermann Verlag 2023
On the Continuity of the Continuous Steiner Symmetrization
Giuseppe Buttazzo
Dip. di Matematica, Università di Pisa, Italy
giuseppe.buttazzo@unipi.it
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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