@Article{ATA-30-296, author = {}, title = {Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {3}, pages = {296--305}, abstract = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.6}, url = {http://global-sci.org/intro/article_detail/ata/4494.html} }