Semilinear PDEs on self-similar fractals

Communications in Mathematical Physics

Volumn 206, Issue 1, 1999, Pages 235-245

  Falconer, K J ^a  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033239028     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050703     Document Type: Article

References (21)

1. 1. Ambrosetti, A., Prodi, G.: A Primer of Nonlinear Analysis. Cambridge: University Press, 1992
2. 2. Ambrosetti, A., Rabinowitz, G.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349-381 (1973)
3. 3. Barlow, M.T., Bass, R.F.: Transition densities for Brownian motion on the Sierpiński carpet. Probab. Theory Related Fields 91, 307-330 (1992)
4. 4. Barlow, M.T., Kigami, J.: Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets. J. London Math. Soc.(2) 56, 320-332 (1997)
5. 5. Biroli, M., Mosco, U.: Sobolev and isoperimetric inequalities for Dirichlet forms on discontinuous media. Rend. Mat. Acc. Lincei s. 9 6, 37-44 (1995)
6. 6. Chow, S-N., Hale, J.K.: Methods of Bifurcation Theory. Berlin: Springer, 1982
7. 7. Falconer, K.J.: Fractal Geometry - Mathematical Foundations and Applications. Chichester: John Wiley, 1992
8. 8. Falconer, K.J.: Techniques in Fractal Geometry. Chichester: John Wiley, 1997
9. 9. Hambly, B.M.: Brownian motion on a random recursive Sierpinski gasket. Ann. Probab. 25, 1059-1102 (1997)
10. 10. Kigami, J.: In quest of fractal analysts. In: Yamaguti, M., Hata, M., Kigami, J. (eds.) Mathematics of Fractals, Providence, RI: American Mathematical Society, 1993, pp. 53-73
11. 11. Kigami, J.: Effective resistances for harmonic structures on p.c.f. self-similar sets. Math. Proc. Cambridge Philos. Soc. 115, 291-303 (1994)
12. 12. Kigami, J.: Harmonic calculus on p.c.f. self-similar sets. Trans. Am. Math. Soc. 335, 721-755 (1993)
13. 13. Lions, P.L.: On the existence of positive solutions of semi-linear elliptic equations. SIAM Review. 24, 441-467 (1982)
14. 14. Kigami, J., Lapidus, M.L.: Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar sets. Commun. Math. Phys. 158, 93-125 (1993)
15. 15. Kusuoka, S., Yin, Z.X.: Dirichlet forms on fractals: Poincaré constant and resistance. Probab.Theory Related Fields 93 ,169-196 (1992)
16. 16. Lapidus, M.L.: Analysis on fractals, Laplacians on self-similar sets, noncommutative geometry and spectral dimensions. Topol. Methods Nonlinear Anal. 4, 137-195 (1994)
17. 17. Mosco, U.: Dirichlet forms and self-similarity. In: J. Jost et al. (eds.) New directions in Dirichlet forms. Cambridge: International Press, 1998
18. 18. Mosco, U.: Lagrangian metrics on fractals. Proc. Symp. Appl. Math. 54, 301-323 (1998)
19. 19. Pohozaev, S.: Eigenfunctions of the equation Δu + λf (u) = 0. Soviet. Math. Dokl. 6, 1408-1411 (1965)
20. 20. Posta, G.: Spectral asymptotics for variational fractals. Z. Anal. Anwendungen 17, 417-430 (1998)
21. 21. Strichartz, R.S.: Some properties of Laplacians on fractals. J. Funct. Analysis, to appear