Abstract
The affine Orlicz Polya–Szego principles with respect to Steiner symmetrization and Schwarz symmetrization proved in Lin and Xing (International mathematics research notices, 2019) are extended to $$BV(\Omega )$$ , the space of functions of bounded variation defined in an open set $$\Omega \subset \mathbb {R}^n$$ , and their equality cases are characterized.
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