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... > vector space > topological vector space > normed vector space > Banach space > Sobolev space

mathematical analysis > functional analysis > function space > Sobolev space

set theory > function space > Sobolev space

algebra > linear algebra > function space > Sobolev space

category theory > function space > Sobolev space

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Sobolev space

In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of L^p-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Sobolev_space)

espace de Sobolev

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http://data.loterre.fr/ark:/67375/PSR-H4T13QGZ-9

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