학술논문
On the gradient rearrangement of functions
Document Type
Working Paper
Source
Mathematische Annalen 12 April, 2024
Subject
Language
Abstract
In this paper, we introduce a symmetrization technique for the gradient of a $\BV$ function, which separates its absolutely continuous part from its singular part (sum of the jump and the Cantorian part). In particular, we prove an $\text{\emph{L}}^{\text{1}}$ comparison between the function and its symmetrized. Furthermore, we apply this result to obtain Saint-Venant type inequalities for some geometric functionals.