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.

Absolutely Minimizing Lipschitz Extensions and infinity harmonic functions on the Sierpinski gasket / Camilli, Fabio; Capitanelli, Raffaela; Vivaldi, Maria Agostina. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 163:(2017), pp. 71-85. [10.1016/j.na.2017.07.005]

Absolutely Minimizing Lipschitz Extensions and infinity harmonic functions on the Sierpinski gasket

CAMILLI, FABIO;CAPITANELLI, Raffaela;VIVALDI, Maria Agostina
2017

Abstract

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.
Absolute Minimizing Lipschitz Extension; Infinity Laplacian; McShane–Whitney extensions; Sierpinski gasket; Analysis; Applied Mathematics
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Absolutely Minimizing Lipschitz Extensions and infinity harmonic functions on the Sierpinski gasket / Camilli, Fabio; Capitanelli, Raffaela; Vivaldi, Maria Agostina. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 163:(2017), pp. 71-85. [10.1016/j.na.2017.07.005]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1002934
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