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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, UniversitÓ 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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