Advertisement

A Brief Review of Real and Functional Analysis

  • Hervé Le Dret
Chapter
  • 1.5k Downloads
Part of the Universitext book series (UTX)

Abstract

This chapter is meant to provide a very quick review of the real and functional analysis results that will be most frequently used afterwards. Missing proofs can be found in most classical works dealing with these questions.

References

  1. 1.
    Acerbi, E., Fusco, N.: Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Anal. 62, 371–387 (1984)Google Scholar
  2. 2.
    Adams, R.A.: Sobolev Spaces. Academic Press, New York (1975)Google Scholar
  3. 3.
    Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Commun. Pure Appl. Math. 12, 623–727 (1959)Google Scholar
  4. 4.
    Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Commun. Pure Appl. Math. 17, 35–92 (1964)Google Scholar
  5. 5.
    Ball, J.M.: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63, 337–403 (1977)Google Scholar
  6. 6.
    Ball, J.M.: A version of the fundamental theorem for Young measures. In: PDEs and Continuum Models of Phase Transitions (Nice, 1988). Lecture Notes in Physics, vol. 344, pp. 207–215. Springer, Berlin (1989)Google Scholar
  7. 7.
    Ball, J.M., Currie, J.C., Olver, P.J.: Null Lagrangians, weak continuity, and variational problems of arbitrary order. J. Funct. Anal. 41, 135–174 (1981)Google Scholar
  8. 8.
    Bourbaki, N.: Espaces vectoriels topologiques. Hermann, Paris (1967)Google Scholar
  9. 9.
    Brezis, H.: Équations et inéquations non linéaires dans les espaces vectoriels en dualité. Ann. Inst. Fourier (Grenoble) 18, 115–175 (1968)Google Scholar
  10. 10.
    Brezis, H.: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Mathematics Studies, vol. 5. Notas de Matemática, vol. 50. North-Holland Publishing Co., Amsterdam; American Elsevier Publishing Co., Inc., New York (1973)Google Scholar
  11. 11.
    Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011)Google Scholar
  12. 12.
    Browder, F.: Problèmes non linéaires. Université de Montréal (1966)Google Scholar
  13. 13.
    Buttazzo, G., Giaquinta, M., Hildebrandt, S.: One-Dimensional Variational Problems, An Introduction. Oxford Lecture Series in Mathematics and Its Applications, vol. 15. Clarendon Press, Oxford (1998)Google Scholar
  14. 14.
    Caffarelli, L.A.: The obstacle problem revisited. J. Fourier Anal. Appl. 4, 383–402 (1988)Google Scholar
  15. 15.
    Chazarain, J., Piriou, A.: Introduction à la théorie des équations aux dérivées partielles linéaires. Gauthier-Villars, Paris (1981)Google Scholar
  16. 16.
    Ciarlet, P.G.: Mathematical Elasticity. Vol. I. Three-dimensional Elasticity. Studies in Mathematics and Its Applications, vol. 20. North-Holland Publishing Co., Amsterdam (1988)Google Scholar

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

Personalised recommendations