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Results tagged with sobolev-spaces
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user 8799
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.
7
votes
1
answer
189
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Limit case of Sobolev space in $1$-D
This might look too an elementary question, but I am confined and is not able to find a textbook which answers the following question.
I have a function $f:{\mathbb R}\rightarrow{\mathbb R}$, such …
- 52.3k
23
votes
1
answer
522
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A characterization of constant functions
In How to recognize constant functions. Connections with Sobolev spaces (Russian Math Surveys 57 (2002); MSN), H. Brezis recalls the following fact:
Let $\Omega\subset{\mathbb R}^N$ be connected a …
- 52.3k