# Sobolev spaces on Riemannian manifold

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

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