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Erschienen in:
1998 | OriginalPaper | Buchkapitel
Integration by Parts. Weak Derivatives. Sobolev Spaces
verfasst von : Jürgen Jost
Erschienen in: Postmodern Analysis
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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Weak derivatives are introduced by taking the rule for integration by parts as a definition. Spaces of functions that are in Lp together with certain weak derivatives are called Sobolev spaces. Sobolev’s embedding theorem says that such functions are continuous if their weak derivatives satisfy strong enough integrability properties. Rellich’s compactness theorem says that integral bounds on weak derivatives imply convergence of subsequences of the functions itself in Lp.