Sobolev Spaces

  • Susanne C. Brenner
  • L. Ridgway Scott
Part of the Texts in Applied Mathematics book series (TAM, volume 15)


This chapter is devoted to developing function spaces that are used in the variational formulation of differential equations. We begin with a review of Lebesgue integration theory, upon which our notion of “variational” or “weak” derivative rests. Functions with such “generalized” derivatives make up the spaces commonly referred to as Sobolev spaces. We develop only a small fraction of the known theory for these spaces — just enough to establish a foundation for the finite element method.


Banach Space Sobolev Space Cauchy Sequence Lebesgue Space Lipschitz Domain 


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Susanne C. Brenner
    • 1
  • L. Ridgway Scott
    • 2
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.University of ChicagoChicagoUSA

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