Abstract
AbstractIn this paper, we introduce a symmetrization technique for the gradient of a $$\text {BV}$$ BV function, which separates its absolutely continuous part from its singular part (sum of jump and Cantorian part). In particular, we prove a $$\text {L }^{\text {1}}$$ L 1 comparison between the function and the symmetrization just mentioned. Furthermore, we apply this result to obtain Saint-Venant type inequalities for some geometric functionals.
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