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In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem 1 2 max q ∈ V m , p { f (q) } + 1 2 min q ∈ V m , p { f (q) } − f (p) = 0 in the Sierpiński gasket with prescribed values f (p 1) , f (p 2) and f (p 3) 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. [ABSTRACT FROM AUTHOR]