Rigidity for perimeter inequality under spherical symmetrisation

Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogonal transformations) of the extremals is provided. This is obtained through a careful analysis of the equality cases, an...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2020-08, Vol.59 (4), Article 139
Main Authors: Cagnetti, F., Perugini, M., Stöger, D.
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Rigidity
Systems Theory
Theoretical
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Summary:Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogonal transformations) of the extremals is provided. This is obtained through a careful analysis of the equality cases, and studying fine properties of the circular symmetrisation, which was firstly introduced by Pólya in 1950.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-020-01786-6