A concept of energy Banach space and its application to the gradient method

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The notion of energy Banach space is introduced for nonlinear operators and some properties are discussed. The concept is used to extend the gradient method for operators which are not continuous themselves but their transform to a suitable energy space has appropriate continuity and monotonicity properties. Convergence is obtained in the energy norm. The obtained method is applied to quasilinear elliptic boundary value problems.

Original languageEnglish
Pages (from-to)548-563
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - Mar 15 2002



  • Elliptic boundary value problems
  • Energy space
  • Gradient method
  • Monotone operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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