Abstract
We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami (Analysis on fractals. Cambridge Tracts in Mathematics, 2001): 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 Giga et al. (Trans Am Math Soc 367:49–66, 2015).
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The authors wish to thank the anonymous referees for many suggestions, which were useful to improve the overall presentation.
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This work is partially supported by European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN Grant agreement number 264735-SADCO and by Indam-Gnampa.
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Camilli, F., Capitanelli, R. & Marchi, C. Eikonal equations on the Sierpinski gasket. Math. Ann. 364, 1167–1188 (2016). https://doi.org/10.1007/s00208-015-1251-7
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DOI: https://doi.org/10.1007/s00208-015-1251-7