Fundamental Functional Analysis

  • Viorel BarbuEmail author
Part of the Springer Monographs in Mathematics book series (SMM)


The aim of this chapter is to provide some standard basic results pertaining to geometric properties of normed spaces, convex functions, Sobolev spaces, and variational theory of linear elliptic boundary value problems. Most of these results, which can be easily found in textbooks or monographs, are given without proof or with a sketch of proof only.


Banach Space Weak Solution Open Subset Sobolev Space Convex Function 
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.


  1. 1.
    D. Adams, Sobolev Spaces, Academic Press, San Diego, 1975.zbMATHGoogle Scholar
  2. 2.
    S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure Appl. Math., 12 (1959), pp. 623–727.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    L. Ambrosio, N. Fusco, D. Pallara, Functions of Bounded Variations and Free Discontinuous Processes, Oxford University Press, Oxford, UK, 2000.Google Scholar
  4. 4.
    E. Asplund, Average norms, Israel J. Math., 5 (1967), pp. 227–233.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    V. Barbu, Partial Differential Equations and Boundary Value Problems, Kluwer, Dordrecht, 1998.zbMATHGoogle Scholar
  6. 6.
    V. Barbu, T. Precupanu, Convexity and Optimization in Banach Spaces, D. Reidel, Dordrecht, 1986.zbMATHGoogle Scholar
  7. 7.
    H. Brezis, Analyse Fonctionnelle. Théorie et Applications, Masson, Paris, 1983.zbMATHGoogle Scholar
  8. 8.
    H. Brezis, Opérateurs Maximaux Monotones et Semigroupes de Contractions dans un Espace de Hilbert, North-Holland, Amsterdam, 1973.Google Scholar
  9. 9.
    R.E. Edwards, Functional Analysis, Holt, Rinehart and Winston, New York, 1965.zbMATHGoogle Scholar
  10. 10.
    P. Grisvard, Elliptic Problems in Non Smooth Domains, Pitman Advanced Publishing Program, Boston, 1984.Google Scholar
  11. 11.
    J.L. Lions, Quelques Méthodes de Resolution des Problèmes aux Limites Nonlinéaires, Dunod-Gauthier Villars, Paris, 1969.Google Scholar
  12. 12.
    Y. Komura, Nonlinear semigroups in Hilbert spaces, J. Math. Soc. Japan, 19 (1967), pp. 508–520.CrossRefMathSciNetGoogle Scholar
  13. 13.
    G. Köthe, Topological Vector Spaces, Springer-Verlag, Berlin, 1969.zbMATHGoogle Scholar
  14. 14.
    J.J. Moreau, Fonctionnelles Convexes, Seminaire sur les équations aux dérivées partielles, Collège de France, Paris, 1966–1967.Google Scholar
  15. 15.
    R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1969.Google Scholar
  16. 16.
    K. Yosida, Functional Analysis, Springer-Verlag, New York, 1980.zbMATHGoogle Scholar
  17. 17.
    C. Zălinescu, Convex Analysis in General Vector Spaces, World Scientific, Singapore, 2002.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fac. MathematicsAl. I. Cuza UniversityIasiRomania

Personalised recommendations