Analysis on fractal objects (Q865128)

The author tries to establish a ``new analysis'' to study so-called irregular objects often modeled by fractal sets in order to formulate ``differential equation'' on nowhere differentiable sets or functions. Firstly, the analysis on the Sierpiński gasket is shown, includes the approximation of the Sierpiński gasket, the energy form, the Lagrangian, the Laplacian and the spectral asymptotics on the Sierpiński gasket. Then, the note gives remarks on non-self-similar fractals, such as matching self-similar sets and deforming self-similar sets.