We consider an extension to $n$-dimensions of the notion of increasing rearrangement for functions of one variable, and study the behaviour with respect to this operation of some classes of integral functionals. Among other applications, we obtain a simple direct proof of the existence and uniqueness of $n$-dimensional optimal profles for transitions in a phase-separation model with non-local interaction energy.
Some remarks about a notion of rearrangement
ALBERTI, GIOVANNI
2000-01-01
Abstract
We consider an extension to $n$-dimensions of the notion of increasing rearrangement for functions of one variable, and study the behaviour with respect to this operation of some classes of integral functionals. Among other applications, we obtain a simple direct proof of the existence and uniqueness of $n$-dimensional optimal profles for transitions in a phase-separation model with non-local interaction energy.File in questo prodotto:
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