The p-Laplacian on the Sierpinski gasket

Nonlinearity

Volumn 17, Issue 2, 2004, Pages 595-616

  Strichartz, Robert S ^a   Wong, Carto ^b  

^a Cornell University ^*  (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642399829     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/2/014     Document Type: Article

References (15)

1. [ASST] Adams B, Smith S A, Strichartz R and Teplyaev A 2003 The spectrum of the Laplacian on the pentagasket Trends in Mathematics: Fractals in Graz 2001 (Basle: Birkhauser) pp 1-24
2. [AA] Garzia Azorero J P and Peral Alonso I 1987 Existence and nonuniqueness for the p-Laplacian eigenvalues Commun. Partial Diff. Eqns 12 1389-430
3. [Ba] Barlow M 1998 Diffusion on Fractals (Lecture Notes in Mahematics vol 1690) (Berlin: Springer)
4. [BST] Ben-Bassat O, Strichartz R and Teplyaev A 1999 What is not in the domain of the Laplacian on Sierpinski gasket type fractals J. Fund. Anal. 166 197-217
5. [DSV] Dalrymple K, Strichartz R and Vinson J 1999 Fractal differential equations on the Sierpinski gasket J. Fourier Anal. Appl. 5 203-84
6. [F] Falconer K J 1999 Semilinear PDEs on self-similar fractals Commun. Math. Phys. 206 235-45.
7. [GRS] Gibbons M, Raj A and Strichartz R 2001 The finite element method on the Sierpinski gasket Constructive Approx. 17 561-88
8. [HPS] Herman P E, Peirone R and Strichartz R p-energy and p-harmonic functions on Sierpinski gasket type fractals Potential Anal. at press
9. [Ki1] Kigami J 1989 A harmonic calculus on the Sierpinski gasket Japan. J. Appl. Math. 6 259-90
10. [Ki2] Kigami J 2001 Analysis on Fractals (Cambridge: Cambridge University Press)
11. [OSY] Öberg A, Strichartz R and Yingst A 2002 Level sets of harmonic functions on the Sierpinski gasket Ark. Mat. 40 335-62
12. [Ro] Rockafellar R T 1970 Convex Analysis (Princeton, NJ: Princeton University Press)
13. [S1] Strichartz R 1999 Analysis on fractals Not. Am. Math. Soc. 46 1199-208
14. [S2] Strichartz R 2001 Harmonic mappings of the Sierpinski gasket to the circle Proc. Am. Math. Soc. 130 805-17
15. [SU] Strichartz R and Usher M 2000 Splines on fractals Math. Proc. Camb. Phil. Soc. 129 331-60