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All issues Volume 40 / No 4 (July-August 2006) ESAIM: M2AN, 40 4 (2006) 623-652 References
Free Access
Issue
ESAIM: M2AN
Volume 40, Number 4, July-August 2006
Page(s) 623 - 652
DOI https://doi.org/10.1051/m2an:2006027
Published online 15 November 2006
  1. Y. Achdou, C. Sabot and N. Tchou, A multiscale numerical method for Poisson problems in some ramified domains with a fractal boundary. SIAM Multiscale Model. Simul. (2006) (accepted for publication). [Google Scholar]
  2. Y. Achdou, C. Sabot and N. Tchou, Transparent boundary conditions for Helmholtz equation in some ramified domains with a fractal boundary. J. Comput. Phys. (2006) (in press). [Google Scholar]
  3. R.A. Adams, Sobolev spaces. Academic Press, New York-London (1975). Pure Appl. Math. 65. [Google Scholar]
  4. H. Brezis, Analyse fonctionnelle. Collection Mathématiques Appliquées pour la Maîtrise. Théorie et applications. Masson, Paris, 1983. [Google Scholar]
  5. M. Felici, Physique du transport diffusif de l'oxygène dans le poumon humain. Ph.D. thesis, École Polytechnique (2003). [Google Scholar]
  6. M. Gibbons, A. Raj and R.S. Strichartz, The finite element method on the Sierpinski gasket. Constr. Approx. 17 (2001) 561–588. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Grisvard, Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 24, Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  8. J.E. Hutchinson, Fractals and self-similarity. Indiana Univ. Math. J. 30 (1981) 713–747. [CrossRef] [MathSciNet] [Google Scholar]
  9. P.W. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147 (1981) 71–88. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Jonsson and H. Wallin, Function spaces on subsets of Rn. Math. Rep. 2 (1984) xiv+221. [Google Scholar]
  11. J.B. Keller and D. Givoli, Exact nonreflecting boundary conditions. J. Comput. Phys. 82 (1989) 172–192. [CrossRef] [MathSciNet] [Google Scholar]
  12. M.R. Lancia, A transmission problem with a fractal interface. Z. Anal. Anwendungen 21 (2002) 113–133. [MathSciNet] [Google Scholar]
  13. M.R. Lancia, Second order transmission problems across a fractal surface. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27 (2003) 191–213. [MathSciNet] [Google Scholar]
  14. B.B. Mandelbrodt, The fractal geometry of nature. Freeman and Co (1982). [Google Scholar]
  15. B. Mauroy, M. Filoche, J.S. Andrade and B. Sapoval, Interplay between flow distribution and geometry in an airway tree. Phys. Rev. Lett. 90 (2003). [Google Scholar]
  16. B. Mauroy, M. Filoche, E.R. Weibel and B. Sapoval, The optimal bronchial tree is dangerous. Nature 427 (2004) 633–636. [Google Scholar]
  17. V.G. Maz'ja, Sobolev spaces. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin (1985). Translated from the Russian by T.O. Shaposhnikova. [Google Scholar]
  18. U. Mosco, Energy functionals on certain fractal structures. J. Convex Anal. 9 (2002) 581–600. [MathSciNet] [Google Scholar]
  19. U. Mosco and M.A. Vivaldi, Variational problems with fractal layers. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27 (2003) 237–251. [MathSciNet] [Google Scholar]
  20. R. Oberlin, B. Street and R.S. Strichartz, Sampling on the Sierpinski gasket. Experiment. Math. 12 (2003) 403–418. [MathSciNet] [Google Scholar]
  21. J. Rauch, Partial differential equations. Graduate Texts in Mathematics 128, Springer-Verlag, New York (1991). [Google Scholar]
  22. C. Sabot, Spectral properties of self-similar lattices and iteration of rational maps. Mém. Soc. Math. Fr. (N.S.) 92 (2003) vi+104. [Google Scholar]
  23. C. Sabot, Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices, in Fractal geometry and applications: a jubilee of Benoît Mandelbrot. Part 1, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 72 (2004) 155–205. [Google Scholar]
  24. B. Sapoval and T. Gobron, Vibration of strongly irregular fractal resonators. Phys. Rev. E 47 (1993). [Google Scholar]
  25. B. Sapoval, T. Gobron and A. Margolina, Vibration of fractal drums. Phys. Rev. Lett. 67 (1991). [Google Scholar]

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