Eikonal equations on the Sierpinski gasket

被引：9
|
作者：
Camilli, Fabio [1 ]
Capitanelli, Raffaela [1 ]
Marchi, Claudio [2 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, Via Scarpa 16, I-00161 Rome, Italy
[2] Univ Padua, Dipartimento Ingn Informaz, Via Gradenigo 6-B, I-35131 Padua, Italy
来源：
MATHEMATISCHE ANNALEN | 2016年 / 364卷 / 3-4期
关键词：
HAMILTON-JACOBI EQUATIONS;
D O I：
10.1007/s00208-015-1251-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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).
引用
收藏
页码：1167 / 1188
页数：22
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