Calculus of Variations and Geometric Measure Theory

G. M. Capriani

The Steiner rearrangement in any codimension

created by capriani on 16 Dec 2011
modified on 10 Dec 2012


Accepted Paper

Inserted: 16 dec 2011
Last Updated: 10 dec 2012

Journal: Calc. Var. Partial Differential Equations
Year: 2012


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.