A note on the area and coarea formulas for general volume densities and some applications
Abstract
We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. As applications, we give a short, "euclidean" proof of the anisotropic Sobolev inequality and describe an anisotropic tube formula for hypersurfaces in mathbbRn. A discussion about the first variation of the anisotropic area is also included.
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