Research Of Dirichlet Form On Some Fractal Sets

In this paper, we firstly discuss a new and important method during studying of fractal set—Dirichlet analysis method,Which is a more useful tool intrduced on analysis of fractal recently and is similar to energy form on mathematics analysis. We firstly give the definition of Dirichlet form on fractal set and some therom which is useful to our paper.Through this useful methods and tools, we study the characteristics Dirichlet form of harmonic function defined on self-similar fractal space. The main result of this paper is that the Dirichlet form defined on self-similar fractal sets can be resolved into several part Dirichlet forms.The relation of the total Dirichlet form and part Dirichlet form is that the former can be noted by laters with lines. This result is very different from the relationship in classic mathematics analysis. Though main content on fractal analysis is contruction of differential equations on fractal sets,and the contruction of definition of differential is more difficult, we consider the the definition of Laplace operator, which will use the the definition and characteristics of Dirichlet form. So some characteristics of Dirichlet form is more necessary on fractal analysis.