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I know one can define the Sobolev spaces on a Riemannian manifold as completions, but is there an equivalent definition that uses weak derivatives, like in the case of open sets in $\mathbb{R}^n$ ?

Thanks

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  • $\begingroup$ Intrinisc colocal weak derivatives? arxiv.org/pdf/1312.5858.pdf $\endgroup$ – Kevin Apr 29 '16 at 14:08
  • $\begingroup$ Sure, pick a bunch of charts and use a partition of unity to do the standard thing. $\endgroup$ – user98602 Apr 30 '16 at 3:04

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