We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize this limit function as the unique metric viscosity solution to the eikonal equation on the Sierpinski gasket according to the definition introduced in [3].
Eikonal equations on the Sierpinski gasket / Camilli, Fabio; Capitanelli, Raffaela; Marchi, Claudio. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 364:(2016), pp. 1167-1188. [10.1007/s00208-015-1251-7]
Eikonal equations on the Sierpinski gasket
CAMILLI, FABIO;CAPITANELLI, Raffaela;
2016
Abstract
We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize this limit function as the unique metric viscosity solution to the eikonal equation on the Sierpinski gasket according to the definition introduced in [3].| File | Dimensione | Formato | |
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