TY - JOUR
T1 - Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets
JO - Analysis in Theory and Applications
VL - 3
SP - 296
EP - 305
PY - 2014
DA - 2014/10
SN - 30
DO - http://doi.org/10.4208/ata.2014.v30.n3.6
UR - https://global-sci.org/intro/article_detail/ata/4494.html
KW - p.c.f. self-similar sets, Hölder estimates, harmonic function.
AB - <p style="text-align: justify;">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.</p>