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 [10.1023/A:1026377524793].

p-energy and p-harmonic functions on Sierpinski gasket type fractals

PEIRONE, ROBERTO;
2004

Abstract

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
DIRICHLET FORMS; UNIQUENESS
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 [10.1023/A:1026377524793].
Herman, P; Peirone, R; Strichartz, R
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/31309
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