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Properties of the energy Laplacian on Sierpinski gasket type fractals
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper,we extend some results from the standard Laplacian on the Sierpinski Gasket to the energy Laplacian. We evaluate the pointwise formula for the energy Laplacian and then observe that we have the analogue of Picard’s existence and uniqueness theorem also for the energy Laplacian and we approximate functions vanishing on the boundary with functions vanishing in a neighborhood of the boundary as in [13]. Then we generalize to the level three Sierpinski Gasket SG3 the pointwise formula, the scaling formula for the energy Laplacian and some of the equivalent aforementioned results. 

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Natural Sciences
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Mathematics
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URN: urn:nbn:se:uu:diva-235768OAI: oai:DiVA.org:uu-235768DiVA: diva2:761913
Available from: 2014-11-10 Created: 2014-11-10 Last updated: 2017-02-20Bibliographically approved

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