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Results tagged with sobolev-spaces
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user 90154
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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Equivalence of Sobolev spaces for different metrics
You said you know why the $L^2$ norms are equivalent, so let's look at the gradient term
$$\int |\nabla^{g_1}u|^2,$$
where the norm associated to $|\cdot|$ doesn't matter. But since $u$ is a function, …
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