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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.

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Sobolev embedding theorems on manifolds

For the case of Riemannian manifolds, Hebey wrote a book about it. The main takeaway for Sobolev embeddings(not Morrey): If M is compact, everything is quite fine and works as usually. If M is only co …
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