The Laplacian on p.c.f. self-similar sets via the method of averages

► We show how to define symmetric Laplacian on post critically finite self-similar sets by using the method of averages. ► The approach combined Kigami's method and the method of averages introduced by Kusuoka and Zhou. ► We have generalized Strichartz's results and our previous works. ► A different proof of harmonic extension algorithm is given.