Abstract
For f∈BV(Rn), a function of bounded variation, we establish requirements on f such that its total variation ‖Df‖ is minimal compared to that of its affine transforms of the same Lnn−1 norm. In addition, a weak version of the affine Pólya-Szegö principle on BV(Rn) and a weak affine Sobolev inequalities are established.
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