Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets  

作　　者：Donglei Tang Rui Hu Chunwei Pan 

机构地区：[1]Department of Applied Mathematics, Nanjing Audit University

出　　处：《Analysis in Theory and Applications》2014年第3期296-305,共10页分析理论与应用（英文刊）

基　　金：supported by the grants NSFC11201232, 12KJB110008;Qing Lan Project, 13KJB110015, 12YJAZH096;the Project-sponsored by SRF for ROCS, SEM

摘　　要：In this paper we establish sharp H/51der 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 weU-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.In this paper we establish sharp H/51der 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 weU-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.

关 键 词：p.c.f self-similar sets Hoelder estimates harmonic function. 

分 类 号：O174.3[理学—数学] O189[理学—基础数学]