Sunto
Si dimostra che se una misura, positiva e assolutamente continua, rende valida una certa disuguaglianza isoperimetrica relativa, allora integral del tipo di Dirichlet di funzioni sufficientemente regolari descrescono per effetto di un opportuno riordinamento equidistribuito.
Abstract
We show that if a positive absolutely continous measure causes a special relative isoperimetric inequality to hold, then Dirichlet-type integrals of sufficiently smooth real-valued functions decrease under an appropriate equimeasurable rearrangement.
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