The Steiner rearrangement in any codimension

preprint2012arXivOpen access

Abstract

We analyze the Steiner rearrangement in any codimension of Sobolev and BVBV 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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