Absolutely Minimizing Lipschitz Extensions and infinity harmonic functions on the Sierpinski gasket. (November 2017)

• Record Type: Journal Article
• Authors: Camilli, Fabio; Capitanelli, Raffaela; Vivaldi, Maria Agostina
• Is Part Of: Nonlinear analysis. Volume 163(2017)
• Page Start: 71
• Page End: 85
• Publication Date: 2017-11
• Subjects: 31C20 -- 28A80; Sierpinski gasket -- McShane–Whitney extensions -- Absolute Minimizing Lipschitz Extension -- Infinity Laplacian; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.07.005
• Languages: English
• ISSNs: 0362-546X

Abstract

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.