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Superposition Operators

  • Hervé Le Dret
Chapter
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Part of the Universitext book series (UTX)

Abstract

In the previous chapter, when studying the model problem − Δu = f(u), we have already met operators of the form uf(u) where f is a mapping from \({\mathbb R}\) to \({\mathbb R}\), and u belongs to some function space defined over an open subset of \({\mathbb R}^d\). This type of operator is called a superposition operator or Nemytsky operator. Let us now study these operators in more detail in various functional contexts.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hervé Le Dret
    • 1
  1. 1.Laboratoire Jacques-Louis LionsSorbonne UniversitéParisFrance

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