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Sobolev Spaces

  • Michel Willem
Chapter
Part of the Cornerstones book series (COR)

Abstract

A locally integrable function has a weak derivative of order α when its derivative of order α in the sense of distributions is represented by a locally integrable function. Sobolev spaces are spaces of differentiable functions with integral norms. In order to define complete spaces, we use weak derivatives. The Sobolev embedding theorem is the most important result of this chapter.

Keywords

Weak derivative Sobolev spaces Sobolev inequality Sobolev embedding theorem. 

References

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    Maz’ya, V.: Sobolev Spaces with Applications to Elliptic Partial Differential Equations. Springer, Berlin (2011)zbMATHGoogle Scholar
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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Michel Willem
    • 1
    • 2
  1. 1.Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Académie royale de BelgiqueBrusselsBelgium

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