Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 82)


In this chapter we collect some preliminary results that we will use throughout the rest of the book, such as Fréechet derivatives, superposition operators and eak and classical solutions of linear elliptic equations and their eigenvalues. Sobolev function spaces are also outlined, although a more complete treatment is postponed until Appendix A.


Banach Space Weak Solution Negative Eigenvalue Fredholm Operator Compact Embedding 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.SISSA-International School for Advanced StudiesTriesteItaly
  2. 2.Departamento de Análisis MatemáticoUniversidad de GranadaGranadaSpain

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