In this paper, we introduce a symmetrization technique for the gradient of a BV BV function, which separates its absolutely continuous part from its singular part (sum of jump and Cantorian part). In particular, we prove a L 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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Amato et al. (2024) studied this question.
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