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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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Density on a specific functional space.

I have a question about density. It's probably trivial but I am just learning functional analysis so nothing is trivial to me. Here is my question. Let $$ \mathcal{X}\colon=\mathcal{H}^1(0,1;\mathbb{ …
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