Abstract
We prove weak and strong versions of the coarea formula and the chain rule for distributional Jacobian determinants Ju for functions u in fractional Sobolev spaces Ws,p(Ω), where Ω is a bounded domain in Rn with smooth boundary. The weak forms of the formulae are proved for the range sp>n−1, s≥n−1n, while the strong versions are proved for the range sp>n, s≥nn+1. We also provide a chain rule for the distributional Jacobian determinant of Hölder functions and point out its relation to two open problems in geometric analysis.
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