Sobolev space
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High Quality Content by WIKIPEDIA articles! In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space. Intuitively, a Sobolev space is a Banach space, and in some cases a Hilbert space, of functions with sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and smoothness of a function.…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space. Intuitively, a Sobolev space is a Banach space, and in some cases a Hilbert space, of functions with sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and smoothness of a function.