NONLINEAR MEAN-VALUE FORMULAS ON FRACTAL SETS

Abstract

In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem [Formula: see text] in the Sierpiński gasket with prescribed values [Formula: see text], [Formula: see text] and [Formula: see text] at the three vertices of the first triangle. For this problem we show existence and uniqueness of a continuous solution and analyze some properties like the validity of a comparison principle, Lipschitz continuity of solutions (regularity) and continuous dependence of the solution with respect to the prescribed values at the three vertices of the first triangle.