Author:
Cagnetti F.,Perugini M.,Stöger D.
Abstract
AbstractNecessary 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference31 articles.
1. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000)
2. Barchiesi, M., Cagnetti, F., Fusco, N.: Stability of the Steiner symmetrization of convex sets. J. Eur. Math. Soc. 15, 1245–1278 (2013)
3. Bartsch, T., Weth, T., Willem, M.: Partial symmetry of least energy nodal solutions to some variational problems. J. Anal. Math. 96, 1–18 (2005)
4. Baernstein, A.: A unified approach to symmetrization. Symp. Math. 35, 47–91 (1995)
5. Birindelli, I., Leoni, F., Pacella, F.: Symmetry and spectral properties for viscosity solutions of fully nonlinear equations. J. Math. Pures Appl. 107(9), 409–428 (2017)
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