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Preliminary Results

  • Hermann Sohr
Chapter
  • 1.8k Downloads
Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Abstract

We consider some basic facts on Sobolev spaces without proof. First we collect several inequalities which compare the L q -norm of a function u with the L q -norm of its gradient
$$ \nabla u = ({D_1}u,...,{D_n}u)$$
. Such estimates are called Poincaré estimates. For the proofs we refer to [Nec67], [Agm65], [Ada75], and [Fri69].

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Hermann Sohr
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität PaderbornPaderbornSwitzerland

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