Y. Achdou, T. Deheuvels, and N. Tchou, Extensions and traces for a class of domains with self-similar fractal boundaries

Y. Achdou and N. Tchou, Neumann conditions on fractal boundaries, Asymptotic Analysis, vol.53, issue.1 2, pp.61-82, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00139849

Y. Achdou and N. Tchou, Trace results on domains with self-similar fractal boundaries, Journal de Math??matiques Pures et Appliqu??es, vol.89, issue.6, pp.596-623, 2008.
DOI : 10.1016/j.matpur.2008.02.008
URL : https://hal.archives-ouvertes.fr/hal-00202658

Y. Achdou and N. Tchou, Trace Theorems for a Class of Ramified Domains with Self-Similar Fractal Boundaries, SIAM Journal on Mathematical Analysis, vol.42, issue.4, pp.1449-1482, 2010.
DOI : 10.1137/090747294
URL : https://hal.archives-ouvertes.fr/hal-00353135

R. A. Adams and J. J. Fournier, Sobolev spaces, Pure and Applied Mathematics, vol.140, 2003.

G. Berger, Eigenvalue Distribution of Elliptic Operators of Second Order with Neumann Boundary Conditions in a Snowflake Domain, Mathematische Nachrichten, vol.20, issue.1, pp.11-32, 2000.
DOI : 10.1002/1522-2616(200012)220:1<11::AID-MANA11>3.0.CO;2-Q

K. Falconer, Techniques in fractal geometry, 1997.

K. J. Falconer, The geometry of fractal sets, volume 85 of Cambridge Tracts in Mathematics, 1986.

P. W. Jones, Quasiconformal mappings and extendability of functions in sobolev spaces, Acta Mathematica, vol.147, issue.0, pp.71-88, 1981.
DOI : 10.1007/BF02392869

A. Jonsson, Wavelets on fractals and besov spaces, The Journal of Fourier Analysis and Applications, vol.3, issue.3, pp.329-340, 1998.
DOI : 10.1007/BF02476031

A. Jonsson, Haar wavelets of higher order on fractals and??regularity of functions, Journal of Mathematical Analysis and Applications, vol.290, issue.1, pp.86-104, 2004.
DOI : 10.1016/j.jmaa.2003.09.071

A. Jonsson and H. Wallin, Function spaces on subsets of R n, Math. Rep, vol.2, issue.1, p.221, 1984.

A. Jonsson and H. Wallin, The dual of Besov spaces on fractals, Studia Math, vol.112, issue.3, pp.285-300, 1995.

J. Kigami, Analysis on fractals, volume 143 of Cambridge Tracts in Mathematics, 2001.

M. R. Lancia, A Transmission Problem with a Fractal Interface, Zeitschrift f??r Analysis und ihre Anwendungen, vol.21, issue.1, pp.113-133, 2002.
DOI : 10.4171/ZAA/1067

M. R. Lancia, Second order transmission problems across a fractal surface, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl, vol.27, issue.5, pp.191-213, 2003.

B. B. Mandelbrot and M. Frame, The Canopy and Shortest Path in a Self-Contacting Fractal Tree, The Mathematical Intelligencer, vol.30, issue.2, pp.18-27, 1999.
DOI : 10.1007/BF03024842

V. G. Maz-'ja, Sobolev spaces, 1985.

P. A. Moran, Additive functions of intervals and Hausdorff measure, Proc. Cambridge Philos. Soc, pp.15-23, 1946.
DOI : 10.2307/1989852

U. Mosco, Dirichlet forms and self-similarity, New directions in Dirichlet forms, pp.117-155, 1998.

U. Mosco, Energy functionals on certain fractal structures, J. Convex Anal, vol.9, issue.2, pp.581-600, 2000.

U. Mosco and M. A. Vivaldi, Variational problems with fractal layers, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl, vol.27, issue.5, pp.237-251, 2003.

R. S. Strichartz, Function spaces on fractals, Journal of Functional Analysis, vol.198, issue.1, pp.43-83, 2003.
DOI : 10.1016/S0022-1236(02)00035-6
URL : http://doi.org/10.1016/s0022-1236(02)00035-6

R. S. Strichartz, Analysis on fractals. Notices Amer, Math. Soc, vol.46, issue.10, pp.1199-1208, 1999.