Sobolev spaces

  • Franck Boyer
  • Pierre Fabrie
Part of the Applied Mathematical Sciences book series (AMS, volume 183)


The first section of this chapter is dedicated to the basic definitions and properties of domains in ℝd. We particularly focus our attention on the case of Lipschitz domains for which we can easily define an integration theory on ∂Ω, the outward unit normal on ∂Ω, and finally prove the Stokes formula which is the keystone of the study of partial differential equations on domains.


Sobolev Space Open Covering Lipschitz Domain Regularity Property Extension Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Franck Boyer
    • 1
  • Pierre Fabrie
    • 2
  1. 1.Laboratoire d’Analyse, Topologie, ProbabilitésAix Marseille UniversitéMarseilleFrance
  2. 2.Institut de Mathématiques de Bordeaux Institut Polytechnique de BordeauxENSEIRB-MATMECAPessacFrance

Personalised recommendations