Lagrangian Energy Forms On A Kind Of Fractals

On the Koch curve and the Sierpinski gasket, people have defined the graph energy form as follow:for all ll,u v∈D(ε), where On more general fractal sets, people also have defined the Lagrangian energy form, that is for all u, v∈D(ε), where LK(u, v) is the Lagrangian measure. Through calculating, give the ex-pression of the Lagrangian energy form on the fractal interpolation curve.In this paper, applying the Lagrangian energy form, we summarize the en-ergy form of fractal sets which couldn’t be constructed by graph energy forms, they are two kinds of non self-similar fractals—one is Koch snowflake by match-ing Koch curve, the other is obtained by deforming Sierpinski gasket. Finally, we construct the energy form of more complicated fractals using both matching and deforming.