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Absolutely Minimizing Lipschitz Extensions and Infinity Harmonic Functions on the Sierpinski gasket

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arxiv 1608.03715 v2 pith:75VDKSBO submitted 2016-08-12 math.AP

Fabio Camilli , Raffaela Capitanelli , Maria Agostina Vivaldi This is my paper · ORCID
classification math.AP
keywords functionsinfinitylipschitzabsolutelyextensiongasketharmonicminimizing
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Aim of this note is to study the infinity Laplace operator and the corresponding Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket in the spirit of the classical construction of Kigami for the Laplacian. We introduce a notion of infinity harmonic functions on pre-fractal sets and we show that these functions solve a Lipschitz extension problem in the discrete setting. Then we prove that the limit of the infinity harmonic functions on the pre-fractal sets solves the Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket.

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