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The Steiner rearrangement in any codimension

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Abstract

We analyze the Steiner rearrangement in any codimension of Sobolev and \(BV\) functions. In particular, we prove a Pólya–Szegő inequality for a large class of convex integrals. Then, we give minimal assumptions under which functions attaining equality are necessarily Steiner symmetric.

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Acknowledgments

This research was funded by the 2008 ERC Advanced Grant no. 226234 Analytic Techniques for Geometric and Functional Inequalities. The author would like to thank M. Barchiesi and L. Brasco for some helpful discussions.

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  1. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126 , Naples, Italy

    Giuseppe Maria Capriani

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  1. Giuseppe Maria Capriani
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Correspondence to Giuseppe Maria Capriani.

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Communicated by L. Ambrosio.

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Capriani, G.M. The Steiner rearrangement in any codimension. Calc. Var. 49, 517–548 (2014). https://doi.org/10.1007/s00526-012-0591-3

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  • DOI: https://doi.org/10.1007/s00526-012-0591-3

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