, Volume 40, Issue 4–6, pp 419–436 | Cite as

Analysis on Fractal Objects



Irregular objects are often modeled by fractals sets. In order to formulate partial differential equations on these nowhere differentiable sets the development of a “new analysis” is necessary. With the help of the model case of the Sierpinski gasket the definition of energy forms and Laplacians on self-similar finitely ramified fractals is explained. Moreover, some results for certain classes of non-self-similar fractals are presented.


Fractals Hausdorff dimension Self-similarity Dirichlet form Laplacian Lagrangian 


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© Springer 2005

Authors and Affiliations

  1. 1.Mathematisches InstitutFriedrich-Schiller-Universität JenaJenaGermany

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