Some properties of Laplacians on fractals (Q1295919)

The author studies an analogue of the Laplacian on a class of self-similar fractals that includes the Sierpiński gasket. Here the author explores some properties of these Laplace operators that are natural analogues of results that are known for the usual Laplacian. The author proves an analogue of Liouville's theorem and gives an explicit algorithm for solving the Dirichlet problem for certain domains in the Sierpiński gasket. Moreover, the author presents a harmonic algorithm which allows him to characterize all harmonic functions on domains mentioned above.