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Analysis on Fractal Objects

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Abstract

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.

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Authors and Affiliations

  1. Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbé-Platz 1–4, D-07740, Jena, Germany

    U. R. Freiberg

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2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05

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Freiberg, U.R. Analysis on Fractal Objects. Meccanica 40, 419–436 (2005). https://doi.org/10.1007/s11012-005-2107-0

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