We show that it is possible to define a notion of p-energy for functions defined on a class of fractals including the Sierpinski gasket (SG) for any value of p, 1 < p < infinity, extending the construction of Kigami for p = 2, as a renormalized limit of modified p-energies on a sequence of graphs. Our proof is non-constructive, and does not settle the question of uniqueness. Based on the p-energy we may define p-harmonic functions as p-energy minimizers subject to boundary conditions, but again uniqueness is only conjectural. We present some numerical data as a complement to our results. This work is intended to pave the way for an eventual theory of p-Laplacians on fractals.
Herman, P.E., Peirone, R., & Strichartz, R.S. (2004). p-energy and p-harmonic functions on Sierpinski gasket type fractals. POTENTIAL ANALYSIS, 20(2), 125-148.
Tipologia: | Articolo su rivista |
Citazione: | Herman, P.E., Peirone, R., & Strichartz, R.S. (2004). p-energy and p-harmonic functions on Sierpinski gasket type fractals. POTENTIAL ANALYSIS, 20(2), 125-148. |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1023/A:1026377524793 |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 2004 |
Titolo: | p-energy and p-harmonic functions on Sierpinski gasket type fractals |
Autori: | |
Autori: | Herman, PE; Peirone, R; Strichartz, RS |
Appare nelle tipologie: | 01 - Articolo su rivista |