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Results tagged with sobolev-spaces
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user 5690
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.
3
votes
1
answer
237
views
Sobolev embedding into measurable functions
Consider the fractional Sobolev space
$$
W^{k,2}(\mathbb R^n):=\big\{f \in \mathcal S'\,\big|\,(1+\|\xi\|)^k\hat f(\xi)\in L^2(\mathbb R^n)\big\}
$$
for some $k\in\mathbb R$, and let $\mathcal M$ deno …
CommunityBot
- 1
33
votes
1
answer
2k
views
For which maps $S^1\to S^1$ is the winding number defined?
There are two classes of maps $S^1\to S^1$ for which I know how to define the winding number:
• Continuous maps:
Using the unique path lifting property of the universal covering map $\mathbb R\to S^ …
- 60.6k