187
Views
5
CrossRef citations to date
0
Altmetric
Original Article

The finite difference method for the heat equation on Sierpiński simplices

&
Pages 1477-1501 | Received 28 Feb 2018, Accepted 20 Aug 2018, Published online: 10 Sep 2018

References

  • K. Dalrymple, R.S. Strichartz, and J.P. Vinson, Fractal differential equations on the Sierpiński Gasket, J. Fourier Anal. Appl. 5(2/3) (1999), pp. 203–284. doi: 10.1007/BF01261610
  • U.R. Freiberg and M.R. Lancia, Energy form on a closed fractal curve, Analysis (Berlin) 23(1) (2004), pp. 115–137.
  • M. Fukushima and T. Shima, On a spectral analysis for the Sierpiński Gasket, Potential Anal. 1 (1992), pp. 1–3. doi: 10.1007/BF00249784
  • M. Gibbons, A. Raj, and R.S. Strichartz, The finite element method on the Sierpiński Gasket, Constr. Approx. 17(4) (2001), pp. 561–588. doi: 10.1007/s00365-001-0010-z
  • J.E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 30 (1981), pp. 713–747. doi: 10.1512/iumj.1981.30.30055
  • J. Kigami, A harmonic calculus on the Sierpiński spaces, Japan J. Appl. Math. 6 (1989), pp. 259–290. doi: 10.1007/BF03167882
  • J. Kigami, Harmonic calculus on p.c.f. self-similar sets, Trans. Amer. Math. Soc. 335 (1993), pp. 721–755.
  • J. Kigami, Analysis on Fractals, Cambridge University Press, Cambridge, 2001.
  • J. Kigami, Harmonic analysis for resistance forms, Japan J. Appl. Math. 204 (2003), pp. 399–444.
  • N. Riane and Cl. David, A spectral study of the Minkowski curve, hal-01527996, 2017.
  • T. Shima, On eigenvalue problems for the random walks on the Sierpiński pre-gasket, Japan J. Indus. Appl. Math. 8 (1991), pp. 127–141. doi: 10.1007/BF03167188
  • R.S. Strichartz, Analysis on fractals, Notices Amer. Math. Soc. 46(8) (1999), pp. 1199–1208.
  • R.S. Strichartz, Taylor approximations on Sierpiński Gasket type fractals, J. Func. Anal. 174 (2000), pp. 76–127. doi: 10.1006/jfan.2000.3580
  • R.S. Strichartz, Differential Equations on Fractals, a Tutorial, Princeton University Press, Princeton, 2006.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.