Skip to main content
SpringerLink
Log in

Random Dirichlet problem: Scalar darcy's law

  • Published:
Potential Analysis Aims and scope Submit manuscript

Abstract

Using Ergodic Theory and Epiconvergence notion, we study the rate of convergence of solutions relative to random Dirichlet problems in domains ofR d with random holes whose size tends to 0. This stochastic analysis allows to extend the results already obtained in the corresponding periodic case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ackoglu, M. A. and Krengel, U.: ‘Ergodic Theorems for Superadditive Processes,’J. Reine. Angew. Math. 323 (1981), 53–67.

    MathSciNet  MATH  Google Scholar 

  2. Allaire, G.: Homogénéisation des équations de Stokes et de Navier-Stokes, Thèse de Doctorat de l'Université Paris VI, Spécialité Mathématiques (1989).

  3. Attouch, H.:Variational Convergence for Functions and Operators, Research Notes in Mathematics, Pitman, London.

  4. Aubin, J. P. and Frankowska, H.:Set Valued Analysis, Birkhäuser (1990).

  5. Brillard, A.: Homogénéisation de quelques équations de la mécanique des milieux continus, Thèse d'état (1990).

  6. Castaing, C. and Valadier, M.:Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer Verlag (1977).

  7. Chabi, E. and Michaille, G.: ‘Ergodic Theory and Application to Non Convex Homogenization,’Set-Valued Analysis 2 (1994), 117–134.

    Article  MathSciNet  MATH  Google Scholar 

  8. Dal Maso, G. and Modica, L.: ‘Nonlinear Stochastic Homogenization and Ergodic Theory,’J. Reine. Angew. Math. 368 (1986), 28–42.

    MathSciNet  MATH  Google Scholar 

  9. Dal Maso, G. and Modica, L.: ‘A general theory of variational functionals,’ inTopics in Functional Analysis 1980–81, by F. Strocchi, E. Zarantonello, E. De Giorgi, G. Dal Maso, L. Modica, Scuola Superiore, Pisa, pp. 149–221.

  10. De Giorgi, E.:Convergence Problems for Functions and Operators, Proc. Int. Meeting on ‘Recent methods in nonlinear analysis’, Rene (1978), ed. E. De Giorgi, E. Magenes, Mosco Pitagora, Bologna, pp. 131–188.

    Google Scholar 

  11. Krengel, U.:Ergodic Theorems, Walter de Gruyter, Studies in Mathematics (1985).

Download references

Author information

Authors and Affiliations

  1. Faculté des Sciences, Université My. Ismail, Meknès, Maroc

    E. Chabi

  2. Laboratoire d'Analyse Convexe, Département de Mathématiques, Université Montpellier II, France

    G. Michaille

Authors
  1. E. Chabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Michaille
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chabi, E., Michaille, G. Random Dirichlet problem: Scalar darcy's law. Potential Anal 4, 119–140 (1995). https://doi.org/10.1007/BF01275586

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01275586

Mathematics Subject Classifications (1991)

Key words

Search

Navigation