Equivalence between Pólya–Szegő and relative capacity inequalities under rearrangement

(2014) Archiv der Mathematik — Vol. 103, n° 4, p. 367−379 (2014)

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Abstract
The transformations of functions acting on sublevel sets that satisfy a Pólya-Szegő inequality are characterized as those being induced by transformations of sets that do not increase the associated capacity.
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Van Schaftingen, J. (2014). Equivalence between Pólya–Szegő and relative capacity inequalities under rearrangement. Archiv der Mathematik, 103(4), 367−379. https://doi.org/10.1007/s00013-014-0695-4 (Original work published 2014)