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Wikipedia definition
1. Sobolev spaceIn mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of L-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.
Read “Sobolev space” on English Wikipedia
Read “ソボレフ空間” on Japanese Wikipedia
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