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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 in vector bundles on non-compact manifolds

Let $(M,g)$ be a smooth (not necessarily compact) Riemannian $n$-manifold. It is well-known that dealing with Sobolev spaces in the general non-compact case becomes tricky, since for instance, there a …