Calculus of Variations and Geometric Measure Theory
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G. Alberti

Some Remarks about a Notion of Rearrangement

created on 12 Oct 1999
modified by alberti on 06 Mar 2007


Published Paper

Inserted: 12 oct 1999
Last Updated: 6 mar 2007

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)
Volume: XXIX (2000)
Pages: 457-472
Year: 1999


In this note we consider a notion of rearrangement which extends to n dimensions the familar notion of increasing rearrangement for functions of one variable, and study the behaviour of some classes of integral functionals with respect to this operation. Among other applications, we obtain a simple direct proof of the existence and uniqueness of n-dimensional optimal profiles for transitions in a phase-separation model with a non-local interaction energy.

Keywords: increasing rearrangement, rearrangement inequalities


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