Category:Sobolev Spaces
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This category contains results about Sobolev Spaces.
Definitions specific to this category can be found in Definitions/Sobolev Spaces.
Let $\openint a b$ be an open real interval.
Let $\map {L^2} {a, b}$ be the Lebesgue space.
Let $f \in \map {L^2} {a, b}$.
Suppose that in the sense of distributions we have that:
- $f, \ldots, f^{\paren n} \in \map {L^2} {a, b}$
where $n \in \N$.
Then the Sobolev space is defined and denoted as:
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- $\map {H^n} {a, b} := \set {f \in \map {L^2} {a, b} : f', \ldots, f^{\paren n} \in \map {L^2} {a, b} }$
and equipped with the Sobolev norm.
Pages in category "Sobolev Spaces"
The following 2 pages are in this category, out of 2 total.