Abstract

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.

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Keywords

  • Steiner symmetrization
  • shape optimization
  • torsional rigidity
  • first eigenvalue
  • Gamma-convergence

Mathematics Subject Classification

49Q10, 35P15, 49R50, 49J45, 49R05

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Suggested citation

G. Buttazzo. “On the Continuity of the Continuous Steiner Symmetrization.” Journal of Convex Analysis 30 (2023), No. 2, 615–626. https://doi.org/10.68381/jca30033

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press LLC.