Analysis on Fractal Objects |
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| Authors: | U. R. Freiberg |
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| Affiliation: | 1. Mathematisches Institut, Friedrich-Schiller-Universit?t Jena, Ernst-Abbé-Platz 1–4, D-07740, Jena, Germany
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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. 2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05 |
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| Keywords: | Fractals Hausdorff dimension Self-similarity Dirichlet form Laplacian Lagrangian |
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