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Results tagged with sobolev-spaces
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user 33028
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.
2
votes
A question on optimal Sobolev inequality.
For bounded domains it follows from the Rellich-Kondrashov compactness theorem $H^1\subset\subset L^p$.
If you denote by
$$
S = \inf \frac{\|u\|{H^1}}{\|u\|_{L^p}}
$$
and take a sequence $\{u_n\}$ …
- 61