Function Spaces

  • Mircea Sofonea
  • Andaluzia Matei
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 18)

We introduce in this chapter the function spaces that will be relevant to the subsequent developments in this monograph. The function spaces to be discussed include spaces of continuous and continuously di.erentiable functions, Lebegue and Sobolev spaces, associated with an open bounded domain \(\Omega\ \subset\ \rm{R^d}\). In order to treat time-dependent problems, we also introduce spaces of vector-valued functions, i.e., spaces of mappings de.ned on a time interval [0, T] \([0,T]\ \subset \rm{R}\) with values into a Banach or Hilbert space X.


Hilbert Space Banach Space Sobolev Space Function Space Lipschitz Domain 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Université de PerpignanLabo. ModélisationPerpignan France
  2. 2.University of CraiovaDept. MathematicsCraiovaRomania

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