Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets (Analysis in Theory and Applications, 2014)
In this paper we establish sharp Hölder estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level $3$ Sierpinski gasket, the hexagasket, the $3$-dimensional Sierpinski gasket, and the Vicsek set are also considered.
Keywords: p.c.f. self-similar sets; Hölder estimates; harmonic function.