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Traces

  • Ulrich Wilbrandt
Chapter
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Abstract

One important property of certain Sobolev spaces is the fact that there is a well defined restriction onto the boundary, even though the boundary has measure zero. Such restrictions are known as traces and allow for prescribed boundary data of solutions of partial differential equations.

References

  1. [ACM14]
    Chérif Amrouche, Philippe G. Ciarlet, and Cristinel Mardare. Remarks on a lemma by Jacques-Louis Lions. C. R. Math. Acad. Sci. Paris, 352(9):691–695, 2014.MathSciNetCrossRefGoogle Scholar
  2. [ACM15]
    Chérif Amrouche, Philippe G. Ciarlet, and Cristinel Mardare. On a lemma of Jacques-Louis Lions and its relation to other fundamental results. J. Math. Pures Appl. (9), 104(2):207–226, 2015.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ulrich Wilbrandt
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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