Calculus of Variations and Geometric Measure Theory

G. Buttazzo

On the continuity of the Continuous Steiner Symmetrization

created by buttazzo on 09 Nov 2022



Inserted: 9 nov 2022
Last Updated: 9 nov 2022

Year: 2022


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: Gamma convergence, shape optimization, Steiner symmetrization, first eigenvalue, Torsional rigidity